Monte Carlo methods in sequential and parallel computing of 2D and 3D Ising model

Because of its complexity, the 3D Ising model has not been given an exact analytic solution so far, as well as the 2D Ising in non zero external field conditions, In real materials the phase transition creates a discontinuity. We analysed the Ising model that presents similar discontinuities. We use Monte Carlo methods with a single spin change or a spin cluster change to calculate macroscopic quantities, such as specific heat and magnetic susceptibility. We studied the differences between these methods. Local MC algorithms (such as Metropolis) perform poorly for large lattices because they update only one spin at a time, so it takes many iterations to get a statistically independent configuration. More recent spin cluster algorithms use c lever ways of finding clusters of sites that c an be updated at once. T he single cluster method is probably the best sequential cluster algorithm. We also used the entropic sampling method to simulate the density of states. This method takes into account all possible configurations, not only the most probable. The entropic method also gives good results in the 3D case. We studied the usefulness of distributed computing for Ising model. We established a parallelization strategy to explore Metropolis Monte Carlo simulation and Swendsen-Wang Monte Carlo simulation of this spin model using the data parallel languages on different platform. After building a computer cluster we made a Monte Carlo estimation of 2D and 3D Ising thermodynamic properties and compare the results with the sequential computing. In the same time we made quantitative analysis such as speed up and efficiency for different sets of combined parameters (e.g. lattice size, parallel algorithms, chosen model).