Related papers: Exact Algorithm for Sampling the 2D Ising Spin Gla…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any…
We introduce an exact algorithm for the computation of spin correlation functions for the two dimensional +/-J Ising spin glass in the ground state. Unlike with the transfer matrix method, there is no particular restriction on the shape of…
Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm…
We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same…
We consider the Sherrington-Kirkpatrick model of spin glasses at high-temperature and no external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We prove that, for any inverse temperature…
Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…
Spin-glasses are Gibbs distributions that have been studied in CS for many decades. Recently, they have gained renewed attention as they emerge naturally in learning, inference, optimisation etc. We consider the Edwards-Anderson (EA)…
We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with…
We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph $G$. The sampling algorithm assumes strong spatial mixing together with subexponential growth…
In this paper we propose and realize (the code is publicly available at https://github.com/Thrawn1985/2D-Partition-Function) an algorithm for exact calculation of partition function for planar graph models with binary spins. The complexity…
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example…