Computer simulation of two continuous spin models using Wang–Landau-Transition-Matrix Monte Carlo algorithm

Monte Carlo simulation using a combination of Wang–Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one-dimensional Lebwohl–Lasher model has an exact solution and we have used this to test the performance of the mixed algorithm (WLTM). The other system we have worked on is the two-dimensional XY-model. The purpose of the present work is to test the performance of the WLTM algorithm in continuous models and to suggest methods for obtaining best results in such systems using this algorithm.