Lowtemperature behavior of the statistics of the overlap distribution in Ising spinglass models
Abstract
Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spinglass models including the infiniterange SherringtonKirkpatrick model, shortrange EdwardsAnderson models in three and four space dimensions, and onedimensional longrange models with diluted powerlaw interactions. We study three longrange models with different powers as follows: The first is approximately equivalent to a shortrange model in three dimensions, the second to a shortrange model in four dimensions, and the third to a shortrange model in the meanfield regime. We study an observable proposed earlier by some of us which aims to distinguish the "replica symmetry breaking" picture of the spinglass phase from the "droplet picture," finding that larger system sizes would be needed to unambiguously determine which of these pictures describes the lowtemperature state of spin glasses best, except for the SherringtonKirkpatrick model, which is unambiguously described by replica symmetry breaking. Finally, we also study the median integrated overlap probability distribution and a typical overlap distribution, finding that these observables are not particularly helpful in distinguishing the replica symmetry breaking and the droplet pictures.
 Publication:

Physical Review B
 Pub Date:
 October 2014
 DOI:
 10.1103/PhysRevB.90.134419
 arXiv:
 arXiv:1408.2482
 Bibcode:
 2014PhRvB..90m4419W
 Keywords:

 75.50.Lk;
 75.40.Mg;
 05.50.+q;
 64.60.i;
 Spin glasses and other random magnets;
 Numerical simulation studies;
 Lattice theory and statistics;
 General studies of phase transitions;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 11 pages, 6 figures