Equilibrium microcanonical annealing for first-order phase transitions

Abstract

A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal firstorder transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient. arXiv:1907.07067v1 [cond-mat.stat-mech]

Russian Supercomputing Days

“…Пиковое соотношение связано с разностью свободных энергий упорядоченных и неупорядоченных фаз. Поскольку существует q разных упорядоченных фаз, то точное значение пикового соотношения в пределе термодинамики равно q при температуре перехода \beta c [31]. За e c была принята средняя энергия, вычисленная по формулам (9) и (10), за \beta = \beta c .…”

Population Annealing Method and Hybrid Supercomputer Architecture

“…In addition, there is an extension of the PA algorithm in which the variable parameter temperature is replaced with the variable parameter energy [12]. This algorithm is based on the program code for GPU from paper [10] and demonstrates the possibility of catching the models' nonequilibrium properties.…”

Measuring glass entropies with population annealing

“…[19]. Population annealing (PA) is a sequential Monte Carlo method [29][30][31][32] similar to nested sampling [33][34][35] that is used to simulate systems with rough free energy landscapes. The general idea of population annealing is to initialize a large ensemble of independent simulations in an easy-to-equilibrate region of parameter space and to anneal towards a difficult-to-equilibrate region.…”

“…In this work we use a "hybrid" resampling method that is similar to that in Ref. [32] in order to reduce the statistical errors associated with the resampling process. In the PA scheme of Ref.…”