Defect Energy with Conjugate Boundary Conditions in Spin Glass Models in Two Dimensions

TL;DR

This paper investigates defect energies in 2D Ising spin glass models using conjugate boundary conditions, predicting different thermodynamic behaviors for $ ext{±}J$ and Gaussian models, supporting the existence of a spin glass phase at finite temperatures.

Contribution

It introduces a novel calculation of defect energies with conjugate boundary conditions and predicts non-zero defect energy in the $ ext{±}J$ model, challenging previous assumptions.

Findings

$ar{ ext{ΔE}}$ converges to a non-zero value in the $ ext{±}J$ model.

$ar{ ext{ΔE}}$ approaches zero in the Gaussian model.

Supports the existence of a finite-temperature spin glass phase in the $ ext{±}J$ model.

Abstract

We calculate the naive defect energy $\Delta E$ of Ising spin glass(SG) models in two dimensions using conjugate boundary conditions. We predict that, in the $\pm J$ model, the averaged value $\bar{\Delta E}$ converges to some non-zero value in the thermodynamic limit in contrast with $\bar{\Delta E} = 0$ in the Gaussian model. This prediction is incompatible with previous ones but supports a recent Monte Carlo prediction of the presence of the SG phase at finite temperatures in the $\pm J$ Ising model. We also calculate the interface free energy to confirm it.