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

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.

13 pages, 7 figures; final version, to appear in J. Stat. Phys

References in corpus (2)

• Energy size effects of two-dimensional Ising spin glasses
• Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass

Cited by in corpus (5)

• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Structure Factor of the 3D Random Field XY Model
• Energy gap of the bimodal two-dimensional Ising spin glass
• Aspect-Ratio Scaling of Domain Wall Entropy for the 2D $\pm J$ Ising Spin Glass