LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

Marco TARZIA

Maître de conférences

Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)

Université Pierre et Marie Curie

Tour 12/13 - 5ème étage, bureau 508, 4 Place Jussieu, 75252 Paris Cedex 05, France

Phone: (+33) 1 44 27 72 40         Fax: (+33) 1 44 27 51 00

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Research interests: Statistical physics of complex and disordered systems; Glass transition; Spin glasses; Anderson localization and random matrices; Frustrated magnetism; Quantum strongly correlated systems; Combinatorial oprimization problems in statistical physics and information theory; Soft matter; Statistical mechanics approach to granular materials; Agent based models for economic instabilities and crises.

Marco TARZIA

Maître de conférences

Laboratoire de Physique Théorique de la Matière Condensée (LPTMC)

Université Pierre et Marie Curie

Tour 12/13 - 5ème étage, bureau 508, 4 Place Jussieu, 75252 Paris Cedex 05, France

Phone: (+33) 1 44 27 72 40         Fax: (+33) 1 44 27 51 00

Email: Cette adresse e-mail est protégée contre les robots spammeurs. Vous devez activer le JavaScript pour la visualiser.

 

Research interests: Statistical physics of complex and disordered systems; Glass transition; Spin glasses; Anderson localization and random matrices; Frustrated magnetism; Quantum strongly correlated systems; Combinatorial oprimization problems in statistical physics and information theory; Soft matter; Statistical mechanics approach to granular materials; Agent based models for economic instabilities and crises.

Cv

Short Bio:

PhD in Physics at the University of Naples (Italy) under the supervision of A. Coniglio (2002-2005)
Post-doc at the School of Physics and Astronomy, University of Manchester, UK (2006)
Post-doc at the Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, France (2007)
Post-doc at the Institut de Physique Theorique, CEA/Saclay, France (2008)
Maitre de Conferences at the Universite Pierre et Marie Curie, France (2008-present)

 

My Cv

My Google Scholar profile

 

 

 

Research

My research activity is focused on complex and disordered classical and quantum systems.
In the following I present a brief summary of my work during the last few years on four specific topics.


Glass transition in molecular liquids: RG approach and Ising-like effective theories

There remains a wide divergence of views concerning the appropriate theoretical framework for understanding the nature of the glass transition. In the ongoing search, the Random First-Order Transition (RFOT) theory has proven to be a strong candidate, establishing what appears to be an intricate mean-field (MF) description of supercooled liquids and glasses. This MF treatment predicts a scenario with two critical temperatures T_A and T_K, the upper one T_A being a dynamical singularity and the lower one T_K a thermodynamic ideal  glass transition characterized by a vanishing of the configurational entropy (i.e., the logarithm of the number of metastable states). To make progress toward a theory of the glass transition, one must, however, go beyond the MF description and include the effect of fluctuations in finite-dimensional systems with finite-range interactions.

Recently we provided a real-space renormalization group (RG) analysis of a replica free-energy Ginzburg-Landau functional which is commonly taken to be in the "universality class" of structural glass formers as it displays the two-temperature scenario at the MF level [23]. Our approximation scheme yields in finite dimensions an ideal glass transition similar to that found in MF. However, along the RG flow, the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.

However, there are two important issues related to this analysis:

1) The Landau-like functional for glass-forming liquids used as initial input in the field-theoretical approach is just a crude approximation. In fact, although at the MF level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of RFOT, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. In a recent work [26] we have clarified the physical reasons for this phenomenon and highlighted the unusual fragility of the RFOT to short-range fluctuations. This study highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.

2) The analysis of [23] is missing a key ingredient to describe supercooled liquids: The "self-induced disorder". Within this line of research, we have recently introduced an approach to derive an effective scalar field theory for the glass transition: the fluctuating field is the overlap between equilibrium configurations. In [28] we have applied it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We have shown that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration.
Of course this is valid if the transition is not destroyed by the disorder. One, therefore, needs to compare the strength of the effective random field to that of the effective surface tension. Numerical simulations can be particularly useful in this respect since they take into account, virtually exactly but for systems of limited size, all fluctuations, providing a way to access some of the parameters of the effctive Ising-like theory. To this aim in [33] we have studied this problem on a toy model (the phi^4 scalar field theory in one dimension) which will likely be useful for tackling more diffcult and still unsolved ones.
 

 

Static properties of 2D spin-ice as a sixteen-vertex model

Many interesting classes of classical and quantum magnetic systems are highly constrained. In particular, geometric constraints lead to frustration and the impossibility of satisfying all competing interactions simultaneously, giving rise to the existence of highly degenerate ground states. In conventional spin-ice, topological frustration arises from the fact that the Ising axes in the unit cell are fixed and different, forced to point towards the centers of neighboring tetrahedra. The configurations that minimize the energy of each tetrahedron are the six states (or vertices) with two-in and two-out pointing spins.

Recently, the interest in spin-ice physics has been boosted by the advent of artificial samples on simpler square lattices. Such 2d ice-type systems should be modeled by the complete  sixteen-vertex model on a square lattice. Few is known about the equilibrium (and dynamic) properties of this model in two and three dimensions. In [25] we have revisited the generic vertex model with defects, i.e. the sixteen-vertex model, and completed its analysis: On the one hand we have studied its static properties on a square lattice by using Monte Carlo simulations in equilibrium, establishing its phase diagram and its critical properties. On the other hand, we have introduced a suitable cluster variational Bethe-Peierls MF approximation, which allows to derive self-consistent equations (the fixed points of which yield all expected phases) and to unveil some of their properties, such as the presence of anisotropic equilibrium fluctuations in the symmetry broken phases.

Two-dimensional Ising-like ice models had no experimental counterpart until recently when it became possible to manufacture artificial samples made of arrays of elongated single-domain ferromagnetic nanoislands frustrated by dipolar interactions. In [27] we have compared the equilibrium and out-of-equilibrium properties of the 16-vertex model with the experimental results, finding excellent agreement between vertex densities in 15 differently grown samples. We have revealed the presence of a second-order phase transition from a conventional high temperature paramagnetic phase to a low temperature staggered anti-ferromagnetic phase. Our results demonstrate that the artificial samples are in usual thermal equilibrium, at least away from the critical point. Such a phase transition could hinder full equilibration, and should be unveiled by measuring long-range spatial correlations in the experiments.

 

 

Anderson localization and Random Matrices

Since  the  well-known  pioneering  applications  of Gaussian random matrices to nuclear spectra, random matrix theory (RMT) has found successful applications in many areas of physics and also in other research fields. The reason for such remarkable versatility is that RMT provides universal results which are independent of the specific probability distribution of the random entries: only a few features that determine the universality class matter. The most commonly studied RMs belong to the Gaussian ensembles. There exists, however, a large set of matrices that fall out of the universality classes based on the Gaussian paradigm. These are obtained when the entries are heavy-tailed i.i.d. random variables. The reference case for this different universality class corresponds to entries that are Lévy distributed.

Understanding the statistical spectral properties of these Lévy matrices is an exciting problem from the mathematical and the physical sides. In [31] we provided a thorough study of Lévy Matrices. By analyzing the self-consistent equation on the probability distribution of the diagonal elements of the resolvent we have established the exact equation determining the localization transition separating high energy localized states from low energy extended states, and obtained the phase diagram. Using arguments based on supersymmetric field theory and Dyson Brownian motion we have shown that the eigenvalue statistics is the same one as of the Gaussian orthogonal ensemble in the whole delocalized phase and is Poisson-like in the localized phase. Our numerics confirm these findings, valid in the limit of infinitely large Lévy Matrices, but also reveal that the characteristic scale governing finite size effects diverges much faster than a power law approaching the transition and is already very large far from it. This leads to a very wide crossover region in which the system looks as if it were in a mixed phase.
 

 

Statistical physics approach to micro and macroeconomy. Agent based models for economic instabilities and crises

Inferring  the  behaviour  of  large  assemblies  from  the  behaviour  of  its  elementary constituents  is  arguably  one  of the most important problems in a host of different disciplines:
physics, material sciences, biology, computer sciences, sociology  and,  of  course,  economics. It is also a notoriously hard problem. Statistical  physics  has developed in the last 150 years essentially to understand this micro-macro link. In the framework of the European project CRISIS (http://crisis.oxalto.co.uk), we have explored the possible types of phenomena that simple macroeconomic Agent-Based models (ABM) can reproduce [29].

We have proposed a methodology, inspired by statistical physics, which offers a key tool to characterize a model: its phase diagram in the space of parameters, which allows one to unveil the skeleton of the ABM. Our major finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high. We introduced a simple framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. This asymmetry can have many causes at the micro-level, for example different hiring and firing costs. If  the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model.  One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-to-sales ratio. This leads to an extremely rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. Finally, once we allow wages to adapt, we observe inflation (in the "good" phase) or deflation (in the "bad" phase).

Given the amount of heterogeneity and randomness in our model AMB, a succession of crisis waves (in absence of any exogenous shocks) is both interesting and surprising, and begs for a convincing theoretical explanation. However, our ABM is too complex to be amenable to analytical treatment. This led us to the bare-bones model described by a Fokker-Planck equation [30] which can be computed exactly using standard mathematical tools. The model exhibits a synchronization transition. We computed exactly the phase diagram of the model and the location of the transition in parameter space. Many modifications and extensions can be studied, confirming that the synchronization transition is extremely robust against various sources of noise or imperfection. Our results are also relevant to a variety of other physical or biological situations where synchronization occurs [32].

Along this line of research, we extended in a minimal way the stylized macroeconomic ABM described above, with the aim of investigating the role and efficacy of monetary policy of a "Central Bank" that sets the interest rate such as to steer the economy towards a prescribed in inflation and employment level [34]. We have first identified and modeled several channels through which interest rates can feed into the behavior of firms and households. We then studied different policy experiments, whereby the Central Bank attempts to reach a target inflation and/or unemployment level using a Taylor rule to set the interest rate. Our major finding is that provided its policy is not too aggressive the Central Bank is successful in achieving its goals. However, the existence of different equilibrium states of the economy, separated by phase boundaries (or "dark corners"), can cause the monetary policy itself to trigger instabilities and be counter-productive. In other words, the Central Bank must navigate in a narrow window: too little is not enough, too much leads to instabilities and wildly oscillating economies. This conclusion strongly contrasts with the prediction of DSGE models.

 

Publications

36. Field-Tuned Order by Disorder in Ising Frustrated Magnets with Antiferromagnetic Interactions
P. C. Guruciaga, M. Tarzia, M. V. Ferreyra, L. F. Cugliandolo, S. A. Grigera, R. A. Borzi
Phys. Rev. Lett. 117, 167203 (2016)

35. Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
G. Biroli, C. Rulquin, G. Tarjus, M. Tarzia
SciPost Phys. 1, 7 (2016)

34. Monetary Policy and Dark Corners in a stylized Agent-Based Model
S. Gualdi, M. Tarzia, F. Zamponi, J.-P. Bouchaud
J. Econ. Interact. Coord. , arXiv:1501.00434

33. Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
C. Rulquin, P. Urbani, G. Tarjus, M. Tarzia
Journal of Statistical Mechanics: Theory and Experiment (JSTAT), 023209 (2016)

32. Spontaneous instabilities and stick-slip motion in a generalized Hebraud-Lequeux model
J.-P. Bouchaud, S. Gualdi, M. Tarzia, F. Zamponi
Soft matter 12, 1230 (2016)

31. Level Statistics and Localization Transitions of Levy Matrices
E. Tarquini, G. Biroli, M. Tarzia
Phys. Rev. Lett. 116,  010601 (2016)

30. Endogenous Crisis Waves: Stochastic Model with Synchronized Collective Behavior
S. Gualdi, J.-P. Bouchaud, G. Cencetti, M. Tarzia, F. Zamponi
Phys. Rev. Lett. 114, 088701 (2015)

29. Tipping Points in Macroeconomic Agent-Based Models
S. Gualdi, M. Tarzia, F. Zamponi, J.-P. Bouchaud
J. Econ. Dyn. Control 50, 29 (2015)

28. Random-field-like criticality in glass-forming liquids
G. Biroli, C. Cammarota, G. Tarjus, M. Tarzia
Phys. Rev. Lett. 112, 175701 (2014)

27. Thermal phase transitions in artificial Spin-Ice
D. Levis, L. Cugliandolo, L. Foini, M. Tarzia
Phys. Rev. Lett. 110, 207206 (2013)

26. Fragility of the mean-field scenario of structural glasses for finite-dimensional disordered spin models
C. Cammarota, G. Biroli, M. Tarzia, G. Tarjus
Phys. Rev. B 87, 064202 (2013)

25. Static properties of 2D spin-ice as a sixteen-vertex model
L. Foini, D. Levis, M. Tarzia, L. Cugliandolo
Journal of Statistical Mechanics: Theory and Experiment (JSTAT), P02026 (2013)

24. Nonlinear dielectric susceptibilities: Accurate determination of the growing correlation volume in supercooled liquids
C. Brun, F. Ladieu, D. L'Hôte, M. Tarzia, G. Biroli, J.-P. Bouchaud
Phys. Rev. B 84, 104204 (2011)

23. Renormalization group analysis of the Random First Order Transition
C. Cammarota, G. Biroli, M. Tarzia, G. Tarjus
Phys. Rev. Lett 106, 115705 (2011)

22. On the solution of a 'solvable' model for an ideal glass of hard spheres displaying a jamming transition
M. Mézard, G. Parisi, M. Tarzia, F. Zamponi
Journal of Statistical Mechanics: Theory and Experiment (JSTAT), P03002 (2011)

21. Anomalous nonlinear response of glassy liquids: General argument and a mode-coupling approach
M. Tarzia, G. Biroli, A. Lefèvre, J.-P. Bouchaud
J. Chem. Phys. 132, 054501 (2010)

20. Anderson model on Bethe lattice: density of states, localization properties and isolated eigenvalue
G. Biroli, G. Semerjian, M. Tarzia
Prog. Theor. Phys. 184, 187 (2010)

19. Bose-Einstein condensation in quantum glasses
G. Carleo, M. Tarzia, F. Zamponi
Phys. Rev. Lett. 103, 215302 (2009)

18. Exact solution of the Bose-Hubbard model on the Bethe lattice
G. Semerjian, M. Tarzia, F. Zamponi
Phys. Rev. B 80, 014524 (2009)

17. Lattice models for colloidal gels and glasses
F. Krzakala, M. Tarzia, L. Zdeborovà
Phys. Rev. Lett. 101, 165702 (2008)

16. The valence bond glass phase
M. Tarzia, B. Biroli
Europhys. Lett. 82, 67008 (2008)

15. Group testing with random pools: phase transitions and optimal strategy
M. Mézard, M. Tarzia, C. Toninelli
J. Stat. Phys. 131, 783 (2008)

14. Statistical mechanics of the hitting set problem
M. Mézard, M. Tarzia
Phys. Rev. E 76, 041124 (2007)

13. Glass phenomenology from the connection to spin glasses
M. Tarzia, M. A. Moore
Phys. Rev. E 75, 031502 (2007)

12. On the absence of the glass transition in two dimensional hard disks
M. Tarzia
Journal of Statistical Mechanics: Theory and Experiment (JSTAT), P01010 (2007)

11. Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids
M. Tarzia, A. Coniglio
Phys. Rev. E 75, 011410 (2007)

10. Columnar and lamellar phases in attractive colloidal systems
A. de Candia, E. Del Gado, A. Fierro, N. Sator, M. Tarzia, A. Coniglio
Phys. Rev. E Rapid Comm. 74, 010403 (2006)

9. Pattern formation and glassy phase in the phi4 theory with screened electrostatic repulsion
M. Tarzia, A. Coniglio
Phys. Rev. Lett. 96, 075702 (2006)

8. Granular segregation under vertical tapping
M. Pica Ciamarra, M. D. De Vizia, A. Fierro, M. Tarzia, M. Nicodemi, A. Coniglio
Phys. Rev. Lett. 96, 058001 (2006)

7. Size segregation in granular media induced by phase transition
M. Tarzia, A. Fierro, M. Nicodemi, M. Pica Ciamarra, A. Coniglio
Phys. Rev. Lett. 95, 078001 (2005)

6. Statistical mechanics of dense granular media
A. Coniglio, A. Fierro, M. Nicodemi, M. Pica Ciamarra, M. Tarzia
J. Phys.: Condens. Matter 17, S2557 (2005)

5. Jamming transition in granular media: A mean field approximation and numerical simulations
A. Fierro, M. Nicodemi, M. Tarzia, A. de Candia, A.Coniglio
Phys. Rev. E 71, 061305 (2005)

4. Segregation in fluidized versus tapped packs
M. Tarzia, A. Fierro, M. Nicodemi, A. Coniglio
Phys. Rev. Lett. 93, 198002 (2004)

3. Glass transition in granular media
M. Tarzia, A. de Candia, A. Fierro, M. Nicodemi, A. Coniglio
Europhys. Lett. 66, 531 (2004)

2. A monodisperse model suitable to study the glass transition
M. Pica Ciamarra, M. Tarzia, A. de Candia, A. Coniglio
Phys. Rev. E 68, 066111 (2003)

1. A lattice glass model with no tendency to crystallize
M. Pica Ciamarra, M. Tarzia, A. de Candia, A. Coniglio
Phys. Rev. E 67, 057105 (2003)
 

 

Conference proceedings

6. Statistical physics of group testing
M. Mézard, M. Tarzia, C. Toninelli
International Workshop on Statistical-Mechanical Informatics
J. Phys.: Conf. Ser. 95, 012019 (2008)

5. Statistical mechanics of dense granular media
M. Pica Ciamarra, A. De Candia, M. Tarzia, A. Coniglio, M. Nicodemi
Advances in Complex Systems 8, 217 (2007)

4. Modulated phases and slow dynamics in attractive colloids
A. Coniglio, M. Tarzia, A. de Candia, E. Del Gado, A. Fierro, N. Sator
Internation Symposium on Nonlinearity, Nonequilibrium and Complexity - Questions and Perspectives in Statistical Physics
Physica A 372, 298 (2006)

3. Jamming in dense granular media
A. Coniglio, A. Fierro, A. de Candia, M. Nicodemi, M. Tarzia, M. Pica Ciamarra
19th Sitges Conference on Jamming, Yielding, and Irreversible Deformation in Condensed Matter
Lecture Notes in Physics 688, 53 (2006)

2. Statistical mechanics approach to the jamming transition in granular materials
A. Coniglio, A. de Candia, A. Fierro, M. Nicodemi, M. Tarzia
International Workshop on Trends and Perspectives in Extensive and Non-Extensive Statistical Mechanics
Physica A 344, 431 (2004)

1. On Edwards' theory of powders
A. Coniglio, A. de Candia, A. Fierro, M. Nicodemi, M. Pica Ciamarra, M. Tarzia
Conference on New Materials and Complexity
Physica A 339, 1 (2004)
 

 

Books' chapters

7. Nonlinear Susceptibility Experiments in a Supercooled Liquid: Evidence of Growing Spatial Correlations Close to T_g
C. Brun, D. L'Hôte, F. Ladieu , C. Crauste-Thibierge, G. Biroli, J-.P. Bouchaud, M. Tarzia
Recent Advances in Broadband Dielectric Spectroscopy (2012)

6. Statistical mechanics of dense granular media
M. Nicodemi, A. Coniglio, A. de Candia, A. Fierro, M. Pica Ciamarra, M. Tarzia
Proceedings of the society of photo-optical instrumentation engeneers, Conference on Complex Systems (2005)

5. Mean field theory of dense granular media
A. Coniglio, A. Fierro, M. Nicodemi, M. Pica Ciamarra, M. Tarzia
Proceedings of the International Conference on Powders & Grains (2005)

4. Unifying approach to the jamming transition in granular media and the glass transition in thermal systems
A. Coniglio, A. de Candia, A. Fierro, M. Nicodemi, M. Pica Ciamarra, M. Tarzia
Proceedings of Complexity, Metastability, and Nonextensivity, 31st Workshop of the International School of Solid State Physics (2004)

3. Statistical Mechanics of granular media and glassy systems
A. Coniglio, A. de Candia, A. Fierro, M. Nicodemi, M. Pica Ciamarra, M. Tarzia
Proceedings of the International School of Physics Enrico Fermi on the Physics of Complex Systems - New Advances and Perspectives (2003)

2. Numerical and mean-field study of a lattice glass model
M. Tarzia, M. Pica Ciamarra, A. de Candia, A. Coniglio
Proceedings of the International School of Physics Enrico Fermi on the Physics of Complex Systems - New Advances and Perspectives (2003)

1. Statistical Mechanics of jamming and segregation in granular media
M. Nicodemi, A. Coniglio, A. de Candia, A. Fierro, M. Pica Ciamarra, M. Tarzia
Proceedings of the Workshop on Unifying Concepts in Granular Media and Glasses (2003), arXiv:0401602

 

Unpublished preprints

2. Comment on "Phase transitions for quenched coupled replicas in a plaquette spin model of glasses"
G. Biroli, G. Tarjus, M. Tarzia, arXiv:1606.08268

1. Difference between level statistics, ergodicity, and localization transitions on the Bethe lattice
A. C. Ribeiro Teixeira, M. Tarzia, arXiv:1211.7334

 

 

Talks

Some recent talks



Critical properties of Anderson localization in high dimensions [pdf]
Renormalization group theory of disordered systems, Paris, July 25-27, 2016

Level statistics, ergodicity, and localization transition of Lévy matrices [pdf]
Quantum many body systems, Random Matrices, ans Disorder, Vienna, June 8-12, 2015

Ising-like effective theories for the glass transition [pdf]
Spin-glasses: an old tool for new problems, Cargèse, August 25 - September 6, 2014

 

 

Links

 

Wind and Physics
The Beg Rohu Summer School of statistical physics and condensed matter