Energy size effects of two-dimensional Ising spin glasses

TL;DR

This study investigates the energy size effects in two-dimensional Ising spin glasses with Gaussian and bimodal interactions, analyzing ground-state energies across various boundary conditions and system sizes to understand scaling behaviors and excitations.

Contribution

It provides precise energy measurements and scaling analysis for different boundary conditions, revealing the influence of boundary types and bond distributions on energy scaling and excitations.

Findings

Gaussian bonds show excellent fit across all boundary conditions.

The stiffness exponent is approximately -0.28 for non-free boundary conditions.

Bimodal bonds exhibit unorthodox scaling corrections, especially with mixed boundary conditions.

Abstract

We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on both axes, and free on one axis and periodic on the other. We find accurate values for bulk-, edge-, and corner-site energies. Fits for the system with Gaussian bonds are excellent for all types of boundary conditions over the whole range of system sizes. In particular, the leading behavior for non-free boundary conditions is governed by the stiffness exponent ~ -0.28 describing the scaling of domain-wall and droplet excitations. For the system with a bimodal distribution of bonds the fit is good for free boundary conditions but worse for other geometries, particularly for periodic-free boundary conditions where there appear to be unorthodox corrections to scaling up to large sizes. Finally, by introducing hard bonds we test explicitly for the Gaussian case the relationship between domain walls and the standard scaling behavior.