Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic

TL;DR

This study investigates the zero-temperature phase of the two-dimensional XY spin glass using a genetic heuristic, revealing a unique ground state, spin-chirality decoupling, and no evidence of multiple pure states.

Contribution

Introduces a genetic embedded matching heuristic to analyze the XY spin glass, providing new insights into its ground state properties and excitation spectrum.

Findings

Unique ground state up to global rotation

Spin and chiral channels have distinct stiffness exponents

No evidence of multiple thermodynamic pure states

Abstract

For many real spin-glass materials, the Edwards-Anderson model with continuous-symmetry spins is more realistic than the rather better understood Ising variant. In principle, the nature of an occurring spin-glass phase in such systems might be inferred from an analysis of the zero-temperature properties. Unfortunately, with few exceptions, the problem of finding ground-state configurations is a non-polynomial problem computationally, such that efficient approximation algorithms are called for. Here, we employ the recently developed genetic embedded matching (GEM) heuristic to investigate the nature of the zero-temperature phase of the bimodal XY spin glass in two dimensions. We analyze bulk properties such as the asymptotic ground-state energy and the phase diagram of disorder strength vs. disorder concentration. For the case of a symmetric distribution of ferromagnetic and antiferromagnetic bonds, we find that the ground state of the model is unique up to a global O(2) rotation of the spins. In particular, there are no extensive degeneracies in this model. The main focus of this work is on an investigation of the excitation spectrum as probed by changing the boundary conditions. Using appropriate finite-size scaling techniques, we consistently determine the stiffness of spin and chiral domain walls and the corresponding fractal dimensions. Most noteworthy, we find that the spin and chiral channels are characterized by two distinct stiffness exponents and, consequently, the system displays spin-chirality decoupling at large length scales. Results for the overlap distribution do not support the possibility of a multitude of thermodynamic pure states.