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

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.

arXiv comment4 pages, 3 figures, RevTeX4, v2: slightly shortened version as published

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• Domain walls and chaos in the disordered SOS model
• One-dimensional infinite component vector spin glass with long-range interactions
• Zero-temperature phase of the XY spin glass in two dimensions: Genetic embedded matching heuristic
• Genetic embedded matching approach to ground states in continuous-spin systems
• Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order
• Approximate ground states of the random-field Potts model from graph cuts
• Spin and chiral stiffness of the XY spin glass in two dimensions
• Quasi-exact ground-state algorithm for the random-field Potts model
• Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm