Related papers: Efficient sampling and counting algorithms for the…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
We consider the problem of sampling from the Potts model on random regular graphs. It is conjectured that sampling is possible when the temperature of the model is in the uniqueness regime of the regular tree, but positive algorithmic…
The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from…
We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems, one of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the…
We propose a notion of contraction function for a family of graphs and establish its connection to the strong spatial mixing for spin systems. More specifically, we show that for anti-ferromagnetic Potts model on families of graphs…
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…
A sampling algorithm is presented that generates spin glass configurations of the 2D Edwards-Anderson Ising spin glass at finite temperature, with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
We study the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation…
Ising and Potts models are an important class of discrete probability distributions which originated from statistical physics and since then have found applications in several disciplines. Simulation from these models is a well known…
We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, $p = 1 - e^{- J/ k_BT}$, in…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or…
We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…
In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…
A new algorithm is presented, which allows to calculate numerically the partition function Z_q of the d-dimensional q-state Potts models for arbitrary real values q>0 at any given temperature T with high precision. The basic idea is to…
We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…
An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the dynamics. This includes, in…