Abstract
We identify the origin, and elucidate the character of the extended time-scales that plague computer simulation studies of first and second order phase transitions. A brief survey is provided of a number of new and existing techniques that attempt to circumvent these problems. Attention is then focused on two novel methods with which we have particular experience: “Wang-Landau sampling” and Phase Switch Monte Carlo. Detailed case studies are made of the application of the Wang-Landau approach to calculate the density of states of the 2D Ising model and the Edwards-Anderson spin glass. The principles and operation of Phase Switch Monte Carlo are described and its utility in tackling ‘difficult’ first order phase transitions is illustrated via a case study of hard-sphere freezing. We conclude with a brief overview of promising new methods for the improvement of deterministic, spin dynamics simulations.
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Wilding, N., Landau, D.P. (2002). Monte Carlo Methods for Bridging the Timescale Gap. In: Nielaba, P., Mareschal, M., Ciccotti, G. (eds) Bridging Time Scales: Molecular Simulations for the Next Decade. Lecture Notes in Physics, vol 605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45837-9_8
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