Parallel Monte-Carlo for Critical Phenomena Description in Many Particle Systems

Abstract

Monte Carlo (MC) methods are widely used to simulate various lattice spin models near the critical (phase transition) point. It serves as a non-perturbative method to verify analytical predictions for the critical exponents in three--dimensional cases, where exact and rigorous analytical solutions are not known. Apart from the critical point, the numerical verification of the Goldstone mode singularity in 3D XY model and other spin models with continuous rotational symmetry also is of interest and is done by the Monte Carlo simulation. One of the most effective algorithms (or, in fact, the most effective one) to simulate the equilibrium properties near and at the critical point is the famous Wolff’s cluster algorithm. However, because of difficulties in its parallelisation, a serial code is usually used here. Project proposes elaboration and implementation an appropriate parrallel Wolff’s algorithm for critical phenomena description in many particle systems. Particularly, it would help in simulation of very large lattices near the critical point, since it requires remarkable computation time and resources.