GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

Abstract

Abstract. The population annealing algorithm is a novel approach to study systems with rough free-energy landscapes, such as spin glasses. It combines the power of simulated annealing, Boltzmann weighted differential reproduction and sequential Monte Carlo process to bring the population of replicas to the equilibrium even in the low-temperature region. Moreover, it provides a very good estimate of the free energy. The fact that population annealing algorithm is performed over a large number of replicas with many spin updates, makes it a good candidate for massive parallelism. We chose the GPU programming using a CUDA implementation to create a highly optimized simulation. It has been previously shown for the frustrated Ising antiferromagnet on the stacked triangular lattice with a ferromagnetic interlayer coupling, that standard Markov Chain Monte Carlo simulations fail to equilibrate at low temperatures due to the effect of kinetic freezing of the ferromagnetically ordered chains. We applied the population annealing to study the case with the isotropic intra-and interlayer antiferromagnetic coupling (J 2 /|J 1 | = −1). The reached ground states correspond to non-magnetic degenerate states, where chains are antiferromagnetically ordered, but there is no long-range ordering between them, which is analogical with Wannier phase of the 2D triangular Ising antiferromagnet.

Estimating the density of states of frustrated spin systems

“…The new algorithm introduced here, which we call EPA, is not based on Markov chains but on the sequential Monte Carlo method. PA was first studied in [53,54] and more recently developed further in [55][56][57][58][59][60][61]. It is based on the initialization of a population of replicas drawn from the equilibrium distribution at high temperatures, which is then subsequently cooled to lower and lower temperatures.…”

Optimization of population annealing Monte Carlo for large-scale spin-glass simulations

“…PAMC, on the other hand, remains a relatively new simulation method. Although careful systematic studies of PAMC [16,18] exist, and the method has been applied broadly [9,[19][20][21], little effort has been made to thoroughly optimize the algorithm. Here we focus on this problem and study various approaches to improve the efficiency of PAMC for large-scale simulations.…”

“…Note that PAMC implemented on graphics processing units has been discussed extensively in Refs. [19,27].…”

Absence of long-range order in a general spin-S kagome lattice Ising antiferromagnet

“…Some studies suggested another phase transition occurring at lower temperatures a to a ferrimagnetic phase (M, −M/2, −M/2), with one sublattice fully ordered and two partially disordered [10,12,21]. On the other hand, several other studies argued that due to linear-chain-like excitations in the system there is a crossover to the low-temperature phase, which is a 3D analog of the 2D Wannier phase [9,13,14,26,27]. In the IATL to SIATL dimensional crossover study it was found that the PD phase can also develop in the system consisting of a sufficiently large but finite number of the IATL layers stacked along the z axis.…”