Numerical study of the two-replica overlap of the 3D Edwards–Anderson Ising spin glass

• Published in: Physica A Vol. 321; no. 1; pp. 49 - 58
• Main Authors: Berg, Bernd A, Billoire, Alain, Janke, Wolfhard
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-04-2003
• Subjects: Edwards–Anderson model; Ising; Multi-self-overlap; Multicanonical; Spin glass; Edwards–Anderson model; Ising; Multicanonical; Multi-self-overlap; Spin glass
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(02)01751-X

We present results of recent high-statistics Monte Carlo simulations of the Edwards–Anderson Ising spin-glass model in three dimensions. The study is based on a non-Boltzmann sampling technique, the multi-self-overlap algorithm which is specifically tailored for sampling rare-event states. We thus concentrate on those properties which are difficult to obtain with standard canonical Boltzmann sampling such as the free-energy barriers
F
B
q
in the probability densities
P
J
(
q) of the Parisi overlap parameter
q and the behavior of the tails of the disorder averaged density
P(
q)=[
P
J
(
q)]
av
. Our results for the tails disagree with mean-field predictions and support extreme order statistics over many orders of magnitude.