The random anisotropy model revisited

Abstract

We revisit the thermodynamic behavior of the random-anisotropy O($N$) model by investigating its large-$N$ limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-$N$ limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible "glassy" phases. Finally we discuss the implications of our findings for the finite-$N$ and finite-temperature systems.

25 pages, 16 figures

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• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Phase transitions in XY models with randomly oriented crystal fields
• Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model