LPTMC Seminars

Beyond power laws and amplitude ratios: Extracting universal scaling functions from
NPFRG and publishing them for experimentalists to use
[Stephen Thornton, Itay Griniasty, Gilles Tarjus, Matthieu Tissier, Kaarthik Varma, Archishman Raju,
David Hathcock, Jaron Kent-Dobias, Anna Barth]

Universal scaling functions are enormously informative about the properties near critical points. They are
rarely calculated or published, partly because universal exponents and amplitude ratios are easier to report
and are directly measured, while universal scaling functions involving marginal or irrelevant variables are
both challenging to measure and hitherto hard to calculate. The functional renormalization group methods
of Jussieu and Uruguay seem ideal – they yield direct measures of the evolution of the free energy and
other properties under coarse graining. But the most studied such function is the fixed-point of the RG,
which does not itself predict the behavior when the temperature shifts from criticality and irrelevant
variables become important. The NPFRG method competes with conformal bootstrap for critical
exponents, and has far more applications, but should have no rival for calculating the scaling functions.
This talk will attempt a nuts-and-bolts approach to generate universal scaling functions relevant for
experimentalists, that could be applicable to all types of renormalization-group flows, with an
implementation of LPA for the 3D Ising model. It rests on studying ‘normal form’ coordinates for the RG
flows near the fixed points. Normal forms are a generalization of the nonlinear scaling fields of Wegner: (t,
u) for the 3D Ising model which linearize the flows. For systems like the tricritical and 4D Ising models
they change variables to a simplest possible nonlinear flow. This coordinate transformation makes the
traditional formula \(F(M, T, ... ) = t^{D\nu} F (M t^{-\beta} , u t^{\omega\nu} )\) (derived by linearizing the flow) an exact
prediction. The method then calculates F by coarse-graining the microscopic free energy to the
macroscopic k=0 limit, using methods which recently have come to fruition.

Motility regulation in active (eco)systems

Active matter describes systems whose constituents generate non-conservative forces on their environment, leading to the wealth of emergent phenomena encountered in the living world. In particular, the regulation of motility at the particle scale, either via external cues or quorum-sensing interactions with peers, can dramatically affect the self-organization of active systems.
In the first part of my talk, I will show how one can bridge the gap between particle-based dynamics and hydrodynamic descriptions of motility-regulated active systems, by deriving generalized Green-Kubo relations for a broad class of motility-regulated active systems. [1,2]
Building on these results, I will investigate the role of random motility regulation in the self-organization of microbial ecosystems consisting of N >> 1 species. Combining particle-based simulations with random matrix theory, I will show how weak, random interactions are sufficient to fragment the ecosystem into distinct, spatially segregated communities. Our results hold for a variety of motility-regulation mechanisms, and highlight the need to characterize the role of motility regulation in experimentally relevant situations. [3]

[1] AD, P. L. Muzzeddu, arXiv 2604.09447 (2026)
[2] AD, P. L. Muzzeddu, arXiv 2604.09453 (2026)
[3] AD, A. Altieri, J. Tailleur, Phys. Rev. E 114, 014404 (2026)

Quantum chaos and complexity in Krylov space

The dynamics of a quantum system is confined to a subspace of the state or operator space, the Krylov space, which is often smaller than the full Hilbert/operator space. Krylov space methods therefore provide a compact and computationally efficient description of quantum evolution, which is particularly useful for nonequilibrium phenomena in many-body systems with large Hilbert spaces. In this talk, I will discuss a notion of complexity defined in Krylov space and its use as a probe of operator growth, quantum chaos, information scrambling, and state evolution in both closed and open quantum systems. Illustrative examples include quantum spin chains, Sachdev–Ye–Kitaev models, and random matrix theory. The talk is based on selected topics from the review article arXiv:2405.09628 (Physics Reports) and more recent developments.