This book explores the broad histogram method (BHM), a novel Monte Carlo analysis for the estimation of the density of states, and extends it to the analysis of systems with continuous degrees of freedom. The book starts with a pedagogical introduction to the most widely used Monte Carlo procedures and a review of the BHM-method for discrete systems. Then, the BHM for continuous systems is proposed and tested by contructing it for the classical XY- and Heisenberg models. Next, the method is applied for the first time to improve finite-size scaling analysis, using the two-dimensional XY-model with Z2 symmetry and the three-dimensional Heisenberg model as testing grounds. Finally, some directions for the extension of the BHM analysis to quantum systems and lattice-gauge theories are given.
We have found BHM an excellent tool for the analysis of both discrete and continuous systems. It is extremely useful to join multiple canonical simulations, and increases the precision of thermodynamic estimates by orders of magnitude with a small increment in CPU time. It is also completely general, and can be used in conjunction with almost any sampling algorithm (microcanonical, canonical, multicanonical, cluster, etc.). We expect that its precision improvement, generality, easy implementation and robustness will make the BHM a preferred tool for the study of many problems of the statistical mechanics and related fields.
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