Spin and chiral stiffness of the XY spin glass in two dimensions

TL;DR

This paper introduces a novel algorithm to accurately compute ground states of the 2D XY spin glass model, enabling detailed analysis of spin and chiral stiffness and addressing longstanding questions about degeneracy and degree decoupling.

Contribution

The study develops the genetic embedded matching (GEM) algorithm for exact ground-state computation, facilitating a comprehensive investigation of spin and chiral properties in the 2D XY spin glass.

Findings

Confirmed extensive ground-state degeneracy.

Identified distinct scaling exponents for spin and chiral stiffness.

Provided evidence for or against spin-chiral decoupling.

Abstract

We analyze the zero-temperature behavior of the XY Edwards-Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a specially tailored evolutionary method, resulting in the genetic embedded matching (GEM) approach, allows for the computation of numerically exact ground states for relatively large systems. This enables a thorough re-investigation of the long-standing questions of (i) extensive degeneracy of the ground state and (ii) a possible decoupling of spin and chiral degrees of freedom in such systems. The new algorithm together with appropriate choices for the considered sets of boundary conditions and finite-size scaling techniques allows for a consistent determination of the spin and chiral stiffness scaling exponents.