Accelerated Algorithms 1: Lattice Models

Abstract

We describe several algorithms that help overcome the long time-scales that limit Monte Carlo simulation studies of phase transitions. In addition to cluster Aipping, “N-fold way”, and multicanonical methods, we describe a quite new approach, “Wang- Landau sampling”, that estimates the density of states directly. Detailed case studies are made of the application of some of these methods near 1st order and 2nd order transitions in 2D Ising and Potts models and to the Edwards-Anderson spin glass. Lastly, we describe promising new methods for the improvement of deterministic, spin dynamics simulations.