Finite-Size Corrections for Ground States of Edwards-Anderson Spin Glasses

TL;DR

This study investigates finite-size effects on ground state energies of Edwards-Anderson spin glasses across multiple dimensions, revealing how corrections scale and comparing results with mean-field predictions and other models.

Contribution

It provides a comprehensive analysis of finite-size corrections in spin glasses at various bond densities and dimensions, connecting these corrections to theoretical predictions and mean-field models.

Findings

Finite-size correction exponent w follows the relation w=1-y/d.

At the percolation threshold, corrections match mean-field predictions as d→∞.

In the glassy phase, correction exponent w differs from the predicted 2/3 for large d.

Abstract

Extensive computations of ground state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3,..,7. Results are presented for bond-densities exactly at the percolation threshold, p=p_c, and deep within the glassy regime, p>p_c, where finding ground-states becomes a hard combinatorial problem. Finite-size corrections of the form 1/N^w are shown to be consistent throughout with the prediction w=1-y/d, where y refers to the "stiffness" exponent that controls the formation of domain wall excitations at low temperatures. At p=p_c, an extrapolation for $d\to\infty$ appears to match our mean-field results for these corrections. In the glassy phase, w does not approach the value of 2/3 for large d predicted from simulations of the Sherrington-Kirkpatrick spin glass. However, the value of w reached at the upper critical dimension does match certain mean-field spin glass models on sparse random networks of regular degree called Bethe lattices.