Obtaining Stiffness Exponents from Bond-diluted Lattice Spin Glasses

TL;DR

This paper evaluates a bond-dilution based finite-size scaling method for accurately determining the stiffness exponent in lattice spin glasses, comparing its effectiveness on hierarchical models and the 3D Edwards-Anderson model.

Contribution

It tests and demonstrates the potential and limitations of a bond-dilution finite-size scaling approach for extracting critical exponents in spin glasses.

Findings

Effective for hierarchical Migdal-Kadanoff lattices with known exponents.

Provides insights into the method's advantages and weaknesses.

Applied to 3D Edwards-Anderson model, highlighting practical challenges.

Abstract

Recently, a method has been proposed to obtain accurate predictions for low-temperature properties of lattice spin glasses that is practical even above the upper critical dimension, $d_c=6$. This method is based on the observation that bond-dilution enables the numerical treatment of larger lattices, and that the subsequent combination of such data at various bond densities into a finite-size scaling Ansatz produces more robust scaling behavior. In the present study we test the potential of such a procedure, in particular, to obtain the stiffness exponent for the hierarchical Migdal-Kadanoff lattice. Critical exponents for this model are known with great accuracy and any simulations can be executed to very large lattice sizes at almost any bond density, effecting a insightful comparison that highlights the advantages -- as well as the weaknesses -- of this method. These insights are applied to the Edwards-Anderson model in $d=3$ with Gaussian bonds.