Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-09-11
Int. J. of Mod. Phys. C 14(3), 285 (2003)
Physics
Condensed Matter
Disordered Systems and Neural Networks
14 pages, 9 figures. Accepted for publication at Int. J. of Mod. Phys. C, issue 14(3)
Scientific paper
10.1142/S0129183103004498
Monte Carlo simulation techniques, like simulated annealing and parallel tempering, are often used to evaluate low-temperature properties and find ground states of disordered systems. Here we compare these methods using direct calculations of ground states for three-dimensional Ising diluted antiferromagnets in a field (DAFF) and three-dimensional Ising spin glasses (ISG). For the DAFF, we find that, with respect to obtaining ground states, parallel tempering is superior to simple Monte-Carlo and to simulated annealing. However, equilibration becomes more difficult with increasing magnitude of the externally applied field. For the ISG with bimodal couplings, which exhibits a high degeneracy, we conclude that finding true ground states is easy for small systems, as is already known. But finding each of the degenerate ground states with the same probability (or frequency), as required by Boltzmann statistics, is considerably harder and becomes almost impossible for larger systems.
Hartmann Alexander K.
Katzgraber Helmut G.
Moreno Jackeline
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