Subextensive singularity in the 2D $\pm J$ Ising spin glass

TL;DR

This study investigates the low-energy states of the 2D ±J Ising spin glass, revealing subextensive singularities and long-range correlations that influence low-temperature thermodynamic behavior.

Contribution

It provides new insights into the low-temperature behavior and correlations in the 2D ±J Ising spin glass, highlighting subextensive singularities and their impact on hyperscaling.

Findings

Heat capacity scales as T^{5.33} near zero temperature.

Long-range correlations between zero-energy domain walls are observed.

Model likely obeys hyperscaling despite zero critical temperature.

Abstract

The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Similar results are found for $p$ = 0.25. Our results indicate that this model probably obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. The existence of the subextensive behavior is attributed to long-range correlations between zero-energy domain walls, and evidence of such correlations is presented.