Reduction of Two-Dimensional Dilute Ising Spin Glasses

TL;DR

This paper applies a reduction method to bond-diluted 2D Ising spin glasses, enabling exact ground state calculations and confirming the stiffness exponent aligns with undiluted cases, supporting its validity for higher dimensions.

Contribution

It introduces and validates a reduction method combined with graph algorithms for accurately studying bond-diluted spin glasses.

Findings

Stiffness exponent y_2 = -0.281(3) consistent with undiluted lattices

Reduction method effectively computes exact ground states for large systems

Supports the use of reduction techniques for higher-dimensional spin glass studies

Abstract

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.