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The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those…
Tailoring the performance of next-generation high entropy materials requires a deep understanding of the competition between entropy-driven random solid solution and enthalpy-driven chemical ordering. Investigating such order and disorder…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…
We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip…
The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic…
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 show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which…
Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Even though parallelization strategies for Monte Carlo simulations of…
Monte Carlo computer simulations are virtually the only way to analyze the thermodynamic behavior of a system in a precise way. However, the various existing methods exhibit extreme differences in their efficiency, depending on model…
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…
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
Parallel tempering Monte Carlo simulations have been applied to a variety of systems presenting rugged free-energy landscapes. Despite this, its efficiency depends strongly on the temperature set. With this query in mind, we present a…
We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…