Related papers: Interaction-correlated random matrices
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of it eigenvalues. In…
A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density…
The entropic sampling dynamics based on the reversible information transfer to and from the environment is applied to the globally coupled Ising model in the presence of an oscillating magnetic field. When the driving frequency is low…
We study coarsening dynamics in the ferromagnetic random bond Ising model in d = 1; 2. We focus on the validity of super-universality and the scaling properties of the response functions. In the d = 1 case, we obtain a complete…
We investigate the zero-temperature quantum phase transition of the random bond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two…
Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the…
We study the averaged product of characteristic polynomials of large random matrices in the Gaussian beta-ensemble perturbed by an external source of finite rank. We prove that at the edge of the spectrum, the limiting correlations involve…
The interaction-induced orbital magnetic response of a nanoscale ring is evaluated for a diffusive system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fr\"{o}hlich interactions is crucial. The…
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including:…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular,…
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct…
Phase transitions, as one of the most intriguing phenomena in nature, are divided into first-order phase transitions (FOPTs) and continuous ones in current classification. While the latter shows striking phenomena of scaling and…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
We prove convergence of renormalized correlations of primary fields, i. e., spins, disorders, fermions and energy densities, in the scaling limit of the critical Ising model in arbitrary finitely connected domains, with fixed (plus or…