Low-Temperature Excitations of Dilute Lattice Spin Glasses

TL;DR

This paper introduces a novel method using bond-diluted lattices and an exact reduction algorithm to accurately determine low-temperature excitation exponents in high-dimensional lattice spin glasses, including previously unexplored dimensions.

Contribution

The paper presents a new scalable approach for calculating excitation exponents in lattice spin glasses across various dimensions, utilizing bond dilution and an exact reduction algorithm.

Findings

Determined the stiffness exponent for d=3 as y_3=0.24(1).

Provided new estimates for d=6 and d=7: y_6=1.1(1), y_7=1.24(5).

Improved understanding of low-temperature excitations in high-dimensional spin glasses.

Abstract

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes $L$ can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions $d=3$, $d=6$ (the upper critical dimension), and $d=7$. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in $d=3$, L=9 in $d=6$, or L=8 in $d=7$. Finite size scaling analysis gives $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.