Critical scaling in random-field systems: 2 or 3 independent exponents?

TL;DR

This paper demonstrates that the critical behavior of random-field systems generally requires more than two exponents to describe, highlighting the importance of rare events overlooked by previous theories, though numerical results are inconclusive.

Contribution

It challenges the two-exponent scaling hypothesis in random-field systems by providing a comprehensive theoretical analysis across the (d,N) domain.

Findings

Two or more independent exponents are needed to describe critical scaling.

Rare events play a crucial role in the critical behavior.

Numerical estimates are consistent with both two-exponent and multi-exponent scenarios.

Abstract

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole (d,N) domain of the d-dimensional random-field O(N) model and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random field Ising model are extremely close to the predictions of the two-exponent scaling, so that the issue cannot be decided on the basis of numerical simulations.