Saturday, April 12
Session Chair: Weijun Xu, Peking University
10:00-11:00 Nikolaos Zygouras (University of Warwick)
Exploring the Critical 2d Stochastic Heat Flow
The Critical 2d Stochastic Heat Flow arises as a non-trivial solution of the Stochastic Heat Equation (SHE) at the critical dimension 2 and at a phase transition point. It is a log-correlated field which is neither Gaussian nor a Gaussian Multiplicative Chaos. We will review the phase transition of the 2d SHE, describe the main points of the construction of the Critical 2d SHF and outline some of its features and related questions. Based on joint works with Francesco Caravenna and Rongfeng Sun.
11:00-11:30 Morning Tea Break
11:30-12:30 Tomohiro Sasamoto (Institute of Science Tokyo)
Large Deviation for Large Spin for Interacting Particle Systems
In recent years several interacting particle systems which have a parameter called a “spin” have been introduced and studied. They include the partial exclusion process, inclusion process and the harmonic model. For this class of models, we propose a new type of large deviation for large spin. We first explain the basic formulation based on the scheme of Feng-Kurtz and calculate the associated Hamiltonian for a few examples. Next we prove the large deviation principle for the case of partial exclusion on a finite lattice. We also show how one can calculate the rate function exactly for the harmonic process by a mapping to a classical integrable system. Connections to the macroscopic fluctuation theory (MFT) will also be discussed. The talk is based on collaborations with Cristian Giardina, Hayate Suda and Kirone Mallick.
12:30-14:30 Lunch Break
Session Chair: Zhennan Zhou, Westlake University
14:30-15:30 Hong Qian (University of Washington)
Stochastic Thermodynamics, Kinematics, and Classical Mechanics
We propose a probabilistic model for a natural law in physics: the Gibbsian statistical thermodynamics. Gibbs’ two separate theories, (i) macroscopic chemical thermodynamics and (ii) statistical mechanics, are unified under the new mathematics based on large deviation theory of iid samples. Extending this model to Markovian samples, an attempt is made to view Lagrange-Hamilton-Jacobi formulation of Newtonian mechanics as a non-random signature via the most probable move into future, the maximal likely move in the past, and the most probable motions connecting past to future, even with time irreversibility. These results suggest a pleasing answer to E. P. Wigner’s “unreasonable effectiveness of mathematics” as a classifier for recurrent motions rather than law(s) coming from the above.
15:30-16:00 Afternoon Tea Break
16:00-17:00 Lei-Han Tang (Westlake University)
The Annealed Sherrington-Kirkpatrick Model: Dynamical Condensation via Coevolution of Spins and the Coupling Matrix
The concept of hidden Mattis phase in annealed spin-glass models was first proposed by Kasai and Okiji 40 years ago [1] but received little attention until recently [2, 3]. Although no thermodynamic transition is expected, the distribution of spin configurations acquires a Mattis-type order at low temperatures, as shown rigorously through a mapping between quenched and annealed models along the Nishimori line [4]. In this study, we investigate the dynamic consequences of the hidden Mattis order using detailed Monte Carlo simulations of the Sherrington-Kirkpatrick (SK) Ising spin-glass model with slowly updated annealed coupling constants. During the simulation, we monitor the eigenvalue spectrum of the instantaneous matrix of coupling constants, and our results generally support predictions based on random matrix theory. We observe a gap in the low-temperature Mattis phase that separates the largest eigenvalue from the rest of the spectrum. The principal eigenvector (i.e., the eigenvector of the largest eigenvalue) defines the instantaneous Mattis order, serving as a site-dependent, heterogeneous mean field for the spins. Hybridization of the first two eigenvectors signals a system-level restructuring of the hidden state, which can be detected from the 2-point and 4-point autocorrelation functions of the spins. Therefore, the hidden Mattis order can be associated with formation of a system-wide condensate of spins that undergoes large-scale, intermittent reorganization in configuration space. We present detailed finite-size scaling analysis to characterize the relevant time scales near and far below the transition temperature[5].
References
[1] Y. Kasai and A. Okiji, Prog. Theor. Phys. 69, 20 (1983).
[2] F. Krzakala and L. Zdeborová, J. Chem. Phys. 134, 034513 (2011).
[3] L. Foini and J. Kurchan, SciPost Phys. 12, 080 (2022).
[4] H. Nishimori, Statistical physics of spin glasses and information processing: an introduction, Oxford U Press, 2001.
[5] Ding Wang and Lei-Han Tang, SciPost Phys. 17, 106 (2024).
