A comparison of the performance of WangLandau-Transition-Matrix algorithm with WangLandau algorithm for the determination of the joint density of states for continuous spin models
Monte Carlo simulation has been performed in a one-dimensional LebwohlLasher model and two-dimensional XY X Y -model using the WangLandau (WL) and the WangLandau-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.
wanglandau joint density of states density of states transition matrix