Related papers: Monte Carlo Methods for the Ferromagnetic Potts Mo…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
We propose Monte Carlo methods to estimate the partition function of the two-dimensional Ising model in the presence of an external magnetic field. The estimation is done in the dual of the Forney factor graph representing the model. The…
We consider the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field. The estimation is done via importance sampling in the dual of the Forney factor graph representing the…
Several strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to…
In this paper, we show analytically that the duality of normal factor graphs (NFG) can facilitate stochastic estimation of partition functions. In particular, our analysis suggests that for the $q-$ary two-dimensional nearest-neighbor Potts…
We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…
Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs.…
The partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and complex factors.
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in…
We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is…
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
The dynamics and behavior of ferromagnets have a great relevance even beyond the domain of statistical physics. In this work, we propose a Monte Carlo method, based on random graphs, for modeling their dilution. In particular, we focus on…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
Importance sampling is a promising variance reduction technique for Monte Carlo simulation based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…