Long-range interactions in a lattice gas automaton model for immiscible fluids

Abstract

Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free-energy landscapes. As Markov chain methods, they are inherently serial computationally. It was demonstrated recently, however, that a combination of independent simulations that communicate weight updates at variable intervals allows for the efficient utilization of parallel computational resources for multicanonical simulations. Implementing this approach for the many-thread architecture provided by current generations of graphics processing units (GPUs), we show how it can be efficiently employed with of the order of 104 parallel walkers and beyond, thus constituting a versatile tool for Monte Carlo simulations in the era of massively parallel computing. We provide the fully documented source code for the approach applied to the paradigmatic example of the two-dimensional Ising model as starting point and reference for practitioners in the field.Program Title: cudamucaProgram Files doi: http://dx.doi.org/10.17632/tzhfpdymv9.1 Licensing provisions: Creative Commons Attribution license (CC BY 4.0)Programming language: C++, CUDAExternal routines/libraries: NVIDIA CUDA Toolkit 6.5 or newerNature of problem: The program determines weights for a multicanonical simulation of the 2D Ising model to result in a flat energy histogram. A final production run with these weights provides an estimate of the density of states of the model.Solution method: The code uses a parallel variant of the multicanonical method employing many parallel walkers that accumulate a common histogram. The resulting histogram is used to determine the weight function for the next iteration. Once the iteration has converged, simulations visit all possible energies with the same probability.Additional comments including restrictions and unusual features: The system size and size of the population of replicas are limited depending on the memory of the GPU device used. Code repository at https://github.com/CQT-Leipzig/cudamuca.