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

TL;DR

This paper investigates the zero-temperature properties of the random-anisotropy model in strong-anisotropy limit, revealing its similarity to the Ising spin-glass and analyzing magnetic order in two and three dimensions.

Contribution

It provides exact ground-state configurations and computes the stiffness exponent, demonstrating the model's phase behavior and absence of magnetic order in low dimensions.

Findings

Stiffness exponent in 2D is approximately -0.275.

Stiffness exponent in 3D is approximately 0.2.

No magnetic order in 2D; likely absent in 3D.

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.