Phase diagram and criticality of the random anisotropy model in the large- N limit

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.

Random-field Ising and O(N) models: theoretical description through the functional renormalization group

“…The nonperturbative FRG approach is also a versatile method that can be applied to the study of other disordered systems. This is for instance readily done for models with with a random mass 74 , random anisotropies 77,126 , for a disordered Bose fluid 129 , and for an elastic manifold in a random environment 130 . More generally, this can be carried out for any disordered model whose local order parameter is a simple field as magnetization, density or displacement.…”

“…4. Higher-order random anisotropies in O(N ) models in equilibrium 77,79,126 When the theory has an underlying continuous O(N ) symmetry, quenched disorder can take the form of random anisotropies that couple to products of field components. If these random anisotropies are only of even ranks, the model has an additional inversion symmetry compared to the random field model studied above in this article.…”

“…It allows for a full description of dimensional-reduction breaking and of QLRO. Interestingly, the RAO(N )M has also a nontrivial behavior with putative "glassy" phases in the large N limit, and this is accessible through an FRG treatment 126 .…”

The random anisotropy model revisited

“…The more general relation between SD equations and 1-PI FRG flow will be analyzed elsewhere. 38 One can check that in the vicinity of the lower critical dimension for ferromagnetism, d = 4, the above equations coincide with the perturbative 1-PI FRG equations derived from the nonlinear sigma model. 7,9,13,25 Indeed in d = 4 + , the minimum of the effective potential, which corresponds to y k = 0, grows as ρ mk ∼ 1/ at and around the fixed point that controls the critical point.…”

Critical Behavior of the Three-Dimensional Random Anisotropy Heisenberg Model

“…However only the case of D < 0 was of main interest in that study. Recent research of the large-m limit reported glassy character of zero-temperature state [54].…”