Numerical construction of the Aizenman-Wehr metastate
Disordered Systems and Neural Networks
2017-07-26 v1 Statistical Mechanics
Abstract
Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a "dispersed" metastate, supported on many thermodynamic states.
Keywords
Cite
@article{arxiv.1704.01390,
title = {Numerical construction of the Aizenman-Wehr metastate},
author = {A. Billoire and L. A. Fernandez and A. Maiorano and E. Marinari and V. Martin-Mayor and J. Moreno-Gordo and G. Parisi and F. Ricci-Tersenghi and J. J. Ruiz-Lorenzo},
journal= {arXiv preprint arXiv:1704.01390},
year = {2017}
}
Comments
5 pages, 5 figures