Ground States and Defect Energies of the Two-dimensional XY Spin Glass from a Quasi-Exact Algorithm

TL;DR

This paper introduces a novel quasi-exact algorithm to determine ground states of the 2D XY spin glass model, revealing non-degenerate ground states and providing precise estimates of spin and chiral stiffness exponents.

Contribution

The authors develop a new embedded-cluster matching algorithm combined with a genetic algorithm for accurate ground state computation in the 2D XY spin glass.

Findings

Ground states are non-degenerate up to a global rotation.

Strong crossover effects influence defect energy scaling.

Estimated spin and chiral stiffness exponents are -0.308(30) and -0.114(16).

Abstract

We employ a novel algorithm using a quasi-exact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin glass model with bimodal coupling distribution for square lattices of up to 28x28 spins. Contrary to previous conjectures, the ground state of each disorder replica is non-degenerate up to a global O(2) rotation. The scaling of spin and chiral defect energies induced by applying several different sets of boundary conditions exhibits strong crossover effects. This suggests that previous calculations have yielded results far from the asymptotic regime. The novel algorithm and the aspect-ratio scaling technique consistently give $\theta_s=-0.308(30)$ and $\theta_c=-0.114(16)$ for the spin and chiral stiffness exponents, respectively.