A New Parallel Algorithm for Monte Carlo Simulations of 2D Ising, Potts and XY Models

course paper for Thermodynamics and Statistical Mechanics, 2021-05-29


The Swendsen-Wang (SW) multi-cluster spin flip algorithm is closely related to connected component labeling and analysis (CCL & CCA) algorithms in computer vision. Recently, a new parallel algorithm: Hardware Accelerated 4-connected CCL & CCA (HA4) was proposed. It utilizes Graphical Processing Units (GPUs) and the Common Unified Device Architecture (CUDA) to conduct CCL & CCA efficiently, and surpasses all previous CCL & CCA algorithms. However, the HA4 identifies only and all adjacent set pixels to be in one component, whereas in the SW algorithm bonds are generated between neighbor spin pairs with a probability. We present a new algorithm that combines the HA4 with the SW, with application to Monte Carlo simulations of 2D Ising and Potts models. The algorithm naturally absorbs periodic boundary conditions (PBC) into consideration. In simulating a 32 * 32 square lattice Ising model with a NVIDIA RTX 2060 graphic card, compared with a currently prevalent CUDA C++ package based on Komura equivalence algorithm, ours is approximately 2.3 times faster.


Tian-Shen He
Yan Chen


The paper is available at here.