Related papers: Measuring free energy in parallel tempering Monte …
The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
The Monte Carlo (MC) estimates of thermal averages are usually functions of system control parameters $\lambda $, such as temperature, volume, interaction couplings, etc. Given the MC average at a set of prescribed control parameters…
Parallel tempering, also known as replica exchange sampling, is an important method for simulating complex systems. In this algorithm simulations are conducted in parallel at a series of temperatures, and the key feature of the algorithm is…
An analytic method for deriving the free energy of a three-dimensional Ising-like system near the critical point in a homogeneous external field is developed in the $\rho^6$ model approximation. The mathematical description proposed for…
We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers…
We analyze a new Monte Carlo method which uses transition matrix in the space of energy. This method gives an efficient reweighting technique. The associated artificial dynamics is a constrained random walk in energy, producing the result…
Markov Chain Monte Carlo methods are algorithms used to sample probability distributions, commonly used to sample the Boltzmann distribution of physical/chemical models (e.g., protein folding, Ising model, etc.). This allows us to study…
Monte Carlo simulations are performed for the S = 1/2 XY and ferro- and antiferromagnetic Heisenberg model in two dimensions using the loop algorithm. Thermodynamic properties of all these models are investigated in wide temperature range.…
Recent progress in simulation methodologies and in computer power allow first principle simulations of condensed systems with Born-Oppenheimer electronic energies obtained by Quantum Monte Carlo methods. Computing free energies and…
Calculations of topological observables in lattice gauge theories with traditional Monte Carlo algorithms have long been known to be a difficult task, owing to the effects of long autocorrelations times. Several mitigation strategies have…
Parallel tempering is popular method for allowing MCMC algorithms to properly explore a $d$-dimensional multimodal target density. One problem with traditional power-based parallel tempering for multimodal targets is that the proportion of…
We study the statistical physics of the classical Ising model in the so-called $\alpha$-R\'enyi ensemble, a finite-temperature thermal state approximation that minimizes a modified free energy based on the $\alpha$-R\'enyi entropy. We begin…
Monte Carlo simulation using a cluster algorithm is used to compute the scaling part of the free energy for a three dimensional O(4) spin model. The results are relevant for analysis of lattice studies of high temperature QCD.
We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function $E_0$ by adding any physical quantity $V$ of interest as a new…
We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte…
A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a…
The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM…
We describe a technique for constraining macroscopic fluctuations in thermodynamic variables well-suited for Monte Carlo (MC) simulations of multiphase equilibria. In particular for multicomponent systems this amounts to a statistical…
We develop a parallel rejection algorithm to tackle the problem of low acceptance in Monte Carlo methods, and apply it to the simulation of the hopping conduction in Coulomb glasses using Graphics Processing Units, for which we also…