Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction

TL;DR

This paper introduces a non-perturbative functional renormalization group method to study the random field O(N) model, revealing the reasons for the failure of dimensional reduction and providing accurate critical exponents across dimensions.

Contribution

The authors develop a non-perturbative FRG approach that explains the breakdown of dimensional reduction in RF models due to non-analytic fixed points, applicable to all N and dimensions.

Findings

Dimensional reduction fails below a critical dimension d_c(N)<6.

Critical exponents deviate from dimensional reduction predictions below d_c(N).

The approach applies to the Ising case and other N values.

Abstract

We have developed a non-perturbative functional renormalization group approach for the random field O(N) model (RFO(N)M) that allows us to investigate the ordering transition in any dimension and for any value of N including the Ising case. We show that the failure of dimensional reduction and standard perturbation theory is due to the non-analytic nature of the zero-temperature fixed point controlling the critical behavior, non-analycity which is associated with the existence of many metastable states. We find that this non-analycity leads to critical exponents differing from the dimensional reduction prediction only below a critical dimension d\_c(N)<6, with d\_c(N=1)>3.