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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Citations
Phase diagram of two-dimensional hard ellipses
TL;DR: The phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations supports first order transition scenarios and observes bimodal probability density functions for the transitions involving quasi-long-range positional ordering.
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Cooperative Couplings between Octahedral Rotations and Ferroelectricity in Perovskites and Related Materials.
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TL;DR: In this article, a dual nature of the Fe-AFD coupling, which turns from competitive to cooperative as the oxygen octahedral rotation (AFD) mode strengthens, occurs in numerous perovskite oxides, and a unified model of such a dual interaction is provided by introducing novel high-order coupling terms and explain the atomistic origin of the resulting new form of ferroelectricity in terms of universal steric mechanisms.
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