Exchange Monte Carlo Method and Application to Spin Glass Simulations
Koji Hukushima,Koji Nemoto +1 more
2.3K
TL;DR: In this article, an efficient Monte Carlo algorithm for simulating a "hardly relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced.
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Abstract: We propose an efficient Monte Carlo algorithm for simulating a “hardly-relaxing” system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replicas is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multi-canonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.
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4K
Nonuniversal critical dynamics in Monte Carlo simulations
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Simulated tempering: a new Monte Carlo scheme
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Multicanonical ensemble: A new approach to simulate first-order phase transitions.
Bernd A. Berg,Thomas Neuhaus +1 more
TL;DR: A numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100 and a high-precision computation of the interfacial free energy per unit area is reported.
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