A comparison of the performance of Wang–Landau-Transition-Matrix algorithm with Wang–Landau algorithm for the determination of the joint density of states for continuous spin models

Monte Carlo simulation has been performed in a one-dimensional Lebwohl–Lasher model and two-dimensional XYXY-model using the Wang–Landau (WL) and the Wang–Landau-Transition-Matrix (WLTM) Monte Carlo methods. Random walk has been performed in the two-dimensional space comprising of energy-order parameter and energy-correlation function and the joint density of states (JDOS) were obtained. From the JDOS the order parameter, susceptibility and correlation function are calculated. Agreement between the results obtained from the two algorithms is very good. The work shows that for the purpose of determination of JDOS, the WLTM method is a good alternative to the WL algorithm.