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 (J2/|J1| = −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.
|Publication status||Published - 2016|
|Event||Mathematical Modeling and Computational Physics - Stará Lesná, Slovakia|
Duration: 13 Jul 2015 → 17 Jul 2015
|Conference||Mathematical Modeling and Computational Physics|
|Abbreviated title||MMCP 2015|
|Period||13/07/15 → 17/07/15|
Bibliographical noteThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0 http://creativecommons.org/licenses/by/4.0/ , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Borovsky, M., Weigel, M., Barash, L. Y., & Zukovic, M. (2016). GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice. 02016. Paper presented at Mathematical Modeling and Computational Physics, Stará Lesná, Slovakia. https://doi.org/10.1051/epjconf/201610802016