The Application Of GPU In Statistical Physics

Statistical Physics is aimed to explain the physical properties of macroscopic objectscomposed of large number of interacting particles from microscopic laws, however, it is animpossible task to calculate statistical average from all possible microscopic states of largenumber of interacting particles directly. The Ising model, raised from the ferromagnetic phasetransition, is very simple that can be exactly solved in2D situation, which showsself-magnetization in the thermodynamic limit, indicating the phase transition can be studiedby statistical methods, creating a precedent for using the lattice statistical models to solvephysical problems. Many problems in physics can be researched by Ising like lattice modelsimplifying these problems to lattice model with discrete, limited degrees of freedom, whichreduces amount of computation, however, considering all the microscopic states is alsounrealistic, thus, random importance sampling of the microscopic states to calculate statisticalaverage, Monte Carlo method is widely used in lattice models. Though unsolved exactly for3D Ising model, it is solved by renormalization group and Monte Carlo method. Monte Carlomethod for Ising model is still in optimization, these improvements can always be ported tolattice models such as lattice QCD.The research of Monte Carlo method develops with the computing capabilities ofcomputers, however, with the improvement of the production process, the size of transistors iscloser and closer to the magnitude of the atom, which makes the raising of the CPU clockslow down and the improvement of CPU’s computing power become slower and slower. Onthe other hand, the GPU with its powerful parallel computing power attracts a large number ofresearchers making general purpose computing on it, the transfer from CPU to GPU need toconsider the adaptability of the algorithms on GPU architecture. Monte Carlo method forlattice models on GPU need to be implemented and vivificated, Ising model is the bestsample.This paper introduces the GPU and CUDA architecture, then implementing GPU-basedMetropolis algorithm to two-and three-dimensional Ising model on six lattices in total,gaining high speedup and design a GPU+CPU heterogeneous hybrid algorithm, fitting thedata from the two algorithms, the critical points and critical exponents are obtained for theselattices.