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

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.