Werner Krauth (ENS Paris)

Infinitesimal Monte Carlo Algorithms and Melting in two dimensions

I show how the lifting principle and a new pairwise decomposition of the Metropolis filter allows one to design a class of powerful rejection-free Markov-chain Monte Carlo algorithms that break detailed balance yet satisfy global balance. These algorithms generalize the recent hard-sphere event-chain Monte Carlo method. As an application, I present recent progress in our understanding of the phase diagram for two-dimensional soft disks, particles interacting with a repulsive power-law pair interaction. These results complement, and confirm, earlier results for hard-disk melting, and lead to a general understanding of melting in two dimensions.

References:

M. Michel, S. C. Kapfer, W. Krauth “Generalized event-chain
Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps” J. Chem. Phys. 140 54116 (2014)

S. C. Kapfer, W. Krauth “Hexatic-liquid coexistence in soft disks” manuscript in preparation (2014)

E. P. Bernard, W. Krauth “Two-step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition” Phys Rev. Letters 107, 155704 (2011)