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 (9)

• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Energy exponents and corrections to scaling in Ising spin glasses
• Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses
• Scalings of domain wall energies in two dimensional Ising spin glasses
• Strong universality and algebraic scaling in two-dimensional Ising spin glasses
• Critical thermodynamics of the two-dimensional +/-J Ising spin glass
• Energy size effects of two-dimensional Ising spin glasses
• Negative scaling dimensions and conformal invariance at the Nishimori point in the +/-J random-bond Ising model
• Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D $\pm J$ Ising Spin Glass

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• The bimodal and Gaussian Ising Spin Glasses in dimension two revisited
• 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