Related papers: Exact Algorithm for Sampling the 2D Ising Spin Gla…

A new method to numerically calculate the $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th…

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic…

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…

We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for…

Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization…

Using the decay of the out equilibrium spin-spin correlation function we compute the equilibrium Edward-Anderson order parameter in the three dimensional binary Ising spin glass in the spin glass phase. We have checked that the…

The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…

We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper…

Using tempered Monte Carlo simulations, we study the the spin-glass phase of dense packings of Ising dipoles pointing along random axes. We consider systems of L^3 dipoles (a) placed on the sites of a simple cubic lattice with lattice…

We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…

We study the d-dimensional random Ising model using a Bethe-Peierls approximation in the framework of the replica method. We take into account the correct interaction only inside replicated clusters of spins. Our ansatz is that the…

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…

For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…

We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number…

We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent…

Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy$_2$Ti$_2$O$_7$. Understanding has been hindered by issues including disorder, glass formation, and…

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time…

Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large…

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…