Research and main results: my work stands at the boundary between field theory and condensed matter physics. My main activity is to use renormalization group techniques and, in particular, nonperturbative renormalization group techniques, in order to elucidate the critical, and more generally the long distance, behaviour of systems coming from statistical, condensed matter, and soft matter physics. I have mainly worked on three different kinds of situations:
- magnetic systems with competing interactions, also named frustrated magnets
- polymerized membranes including isotropic, tubular, disordered membranes
- disordered magnets like diluted Ising model, random field and random anisotropy systems
In all these systems the perturbative approaches have encountered great difficulties to describe the long distance, low energy, physics while nonperturbative techniques, in the form developped by C. Wetterich in the 90's and following the seminal work of K.G. Wilson in the 70's, have been sucessfully used and have allowed to clarify both qualitatively and quantitatively many intriguing situations.
[1] Low-Temperature Properties of Two-Dimensional Frustrated Quantum Antiferromagnets: P. Azaria, B. Delamotte and D. Mouhanna, Phys. Rev. Lett. 68, 1762 (1992).
[2] Low-Temperature Properties of Two-Dimensional Frustrated Quantum Antiferromagnets: P. Azaria, B. Delamotte and D. Mouhanna, Helvetica Physica Acta 65, 458 (1992).
[3] Spin Stiffness of Canted Antiferromagnets: P. Azaria, B. Delamotte, T. Jolicoeur and D. Mouhanna, Phys. Rev. B 45, 12612 (1992).
[4] Spontaneous symmetry breaking in quantum frustrated antiferromagnets: P. Azaria, B. Delamotte and D. Mouhanna, Phys. Rev. Lett. 70, 2483 (1993).
[5] Symmetry breaking and finite size scaling in antiferromagnets: P. Azaria, B. Delamotte and D. Mouhanna, J. de Phys. 3, 291 (1993).
[6] Monte Carlo calculation of the spin stiffness of the two-dimensional Heisenberg model: M. Caffarel, P. Azaria, B. Delamotte and D. Mouhanna, Europhysics Letters 26, 493 (1994).
[7] The Massive CPN Model for frustrated spin systems: P. Azaria, P. Lecheminant and D. Mouhanna, Nuclear Physics B 455, 648 (1995).
[8] Wilson-renormalization-group approach of the principal chiral model around two dimensions: B. Delamotte, D. Mouhanna and P. Lecheminant, Phys. Rev. B 59, 6006 (1999).
[9] Correlated Fermions in a One-Dimensional Quasiperiodic Potential: J. Vidal, D. Mouhanna and T. Giamarchi, Phys. Rev. Lett. 83, 3908 (1999).
[10] Frustrated Heisenberg Magnets: A Nonperturbative Approach : M. Tissier, B. Delamotte and D. Mouhanna Phys. Rev. Lett. 84, 5208 (2000).
[11] Nonperturbative approach to the principal chiral model between two and four dimensions: M. Tissier, D. Mouhanna and B. Delamotte, Phys. Rev. B 61, 15327 (2000).
[12] An exact renormalization group approach to frustrated magnets: M. Tissier, D. Mouhanna and B. Delamotte, Int. J. Mod. Phys. A16, 2131 (2001).
[13] Spin-stiffness and topological defects in two-dimensional frustrated spin systems: M. Caffarel, P. Azaria, B. Delamotte and D. Mouhanna, Phys. Rev. B 64, 014412/1 (2001).
[14] Interactions in quasicristals : J. Vidal, D. Mouhanna and T. Giamarchi, Int. J. Mod. Phys. B15, 1329 (2001).
[15] Interacting fermions in self-similar potentials: J. Vidal, D. Mouhanna and T. Giamarchi, Phys. Rev. B 65, 014201-1--014201-15 (2002).
[16] The randomly dilute Ising model: a nonperturbative approach: M. Tissier, D. Mouhanna, J. Vidal and B. Delamotte, Phys. Rev. B 65 140402-1 (2002).
[17] XY frustrated systems: continuous exponents in discontinuous phase transitions: M. Tissier, B. Delamotte and D. Mouhanna, Phys. Rev. B 67, 134422-1 (2003).
[18] Optimization of the derivative expansion in the nonperturbative renormalization group L. Canet, B. Delamotte, D. Mouhanna, J. Vidal, Phys. Rev. D 67, 065004-1 (2003).
[19] Nonperturbative renormalization group approach to the Ising model : A derivative expansion at order 4: L. Canet, B. Delamotte, D. Mouhanna et J. Vidal, Phys. Rev. B 68, 064421-1 (2003)
[20] Nonperturbative renormalization group approach to frustrated magnets: B. Delamotte, D. Mouhanna, M. Tissier, Phys. Rev. B 69 134413 (2004)
[21] Fustrated magnets in three dimensions: a nonperturbative approach: B. Delamotte, D. Mouhanna, M. Tissier, J. Phys. :Condens. Matter 16 s-883 (2004)
[22] Critical properties of a continuous family of XY noncollinear magnets : A. Peles, B.W. Southern, B. Delamotte, D. Mouhanna and M. Tissier, Phys. Rev. B 69, 220408-1(R) (2004).
[23] Short-time dynamics of a family of XY noncollinear magnets: S. Bekhechi, B.W. Southern, A. Peles, and D. Mouhanna; Phys. Rev. E 74, 016109 (2006).
[24] Fixed points in frustrated magnets revisited ” : B. Delamotte, Y. Holovatch, D. Ivaneyko, D. Mouhanna and M. Tissier, J. Stat. Mech. (2008) P03014.
[25] Crumpling transition and flat phase of polymerized phantom membranes : J.-P. Kownacki and D. Mouhanna, Phys. Rev. E 79, 040101 (2009).
[26] Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems : D. Mouhanna and G. Tarjus, Phys. Rev. E 81, 051101 (2010).
[27] Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions : B. Delamotte, M. Dudka, Yu. Holovatch, and D. Mouhanna, Phys. Rev. B 82, 104432 (2010).
[28] Analysis of the 3d massive renormalization group perturbative expansions : a delicate case : B. Delamotte, M. Dudka, Yu. Holovatch, and D. Mouhanna, Condens. Matter Phys. 13, 43703 (2010).
[29] Crumpled-to-tubule transition in anisotropic polymerized membranes : beyond epsilon-expansion: K. Essafi, J.-P. Kownacki and D. Mouhanna, Phys. Rev. Lett. 106, 128102 (2011).
[29] Non-perturbative renormalization group : basic principles and some applications : D. Mouhanna, B. Delamotte, J.-P. Kownacki, M. Tissier, Mod. Phys. Lett. B, 25, 873 (2011).
[30] Nonperturbative renormalization group approach to Lifshitz critical behaviour: K. Essafi, J.-P. Kownacki and D. Mouhanna, EPL, 98 (2012) 51002.
[31] First-order phase transitions in polymerized phantom membranes: K. Essafi, J.-P. Kownacki and D. Mouhanna, Phys. Rev. E 89, 042101 (2014).
[32] Functional Renormalization Group Approach to non-collinear magnets, B. Delamotte, M. Dudka, D. Mouhanna, S. Yabunaka, Phys. Rev. B 93, 064405 (2016)
[33] The random anisotropy model revisited: D. Mouhanna and G. Tarjus, Phys. Rev. B 94, 214205 (2016)
[34] A glassy phase in quenched disordered graphene and crystalline membranes, arXiv:1708.08364