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

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.

arXiv comment18 pages, RevTex 4, moderately revised version as published

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Cited by in corpus (12)

• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Numerical evidence of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
• Monte Carlo studies of the chiral and spin orderings of the three-dimensional Heisenberg spin glass
• Error estimation and reduction with cross correlations
• Domain-wall excitations in the two-dimensional Ising spin glass
• Domain walls and chaos in the disordered SOS model
• One-dimensional infinite component vector spin glass with long-range interactions
• Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order
• Spin-chirality decoupling in the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Ordering of the Heisenberg spin glass in four dimensions
• Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions
• Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings