Energy exponents and corrections to scaling in Ising spin glasses

TL;DR

This paper investigates the distribution and scaling corrections of ground state energies in various Ising spin glasses, revealing Gaussian tendencies, unique variance growth patterns, and connections to domain-wall exponents.

Contribution

It provides new insights into the probability distribution of ground state energies and their finite-size corrections, linking these to domain-wall exponents and expanding on Migdal-Kadanoff lattices.

Findings

P(E) tends to Gaussian in most models

Variance growth varies across models, e.g., slower in SK model

Corrections to energy scale as a power of system size, related to domain-wall exponent

Abstract

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.