Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Abstract

We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find $\theta =-0.275(5)$ and $\theta \approx 0.2$ respectively in two and three dimensions. These results show that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions our data strongly support the absence of spontaneous magnetization in the infinite-volume limit.

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• Universality of the glassy transitions in the two-dimensional +- J Ising model
• Finite-size scaling in two-dimensional Ising spin glass models
• Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves
• The random anisotropy model revisited
• Spin-glass dynamics: experiment, theory and simulation
• Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model
• Phase transitions in XY models with randomly oriented crystal fields