Related papers: New universality classes for generic higher charac…
Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality…
We study relaxation processes in spin systems near criticality after a quench from a high-temperature initial state. Special attention is paid to the stage where universal behavior, with increasing order parameter emerges from an early…
This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type…
We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. We prove weak Gibbsianity of the renormalized measure and convergence of the…
Via an overparameterized linear model with Gaussian features, we provide conditions for good generalization for multiclass classification of minimum-norm interpolating solutions in an asymptotic setting where both the number of underlying…
We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…
Critical dynamics in film geometry is analyzed within the field-theoretical approach. In particular we consider the case of purely relaxational dynamics (Model A) and Dirichlet boundary conditions, corresponding to the so-called ordinary…
While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for…
We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions tightly linked to the monotone cellular automata called bootstrap percolation. There are three classes of such models,…
Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These…
Critical point of liquid-gas (LG) transition does not conform with the paradigm of spontaneous symmetry breaking because there is no broken symmetry in both phases. This stimulated the ongoing debate about the nature of the universality…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…
We establish new bounds on character values and character ratios for finite groups $G$ of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase…
Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
Understanding universal behavior of far-from-equilibrium transport dynamics at a quantum many body level is a longstanding challenge. In particular, a full characterization of universal dynamics of nonlocal correlation functions still…
It is still a debated issue whether all critical active particles belong to the same universality class. Here we numerically study the critical behavior of quorum sensing active particles that represents the archetypal model for…
Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…