A unified picture of ferromagnetism, quasi-long range order and criticality in random field models

TL;DR

This paper uses a nonperturbative functional renormalization group approach to explore phase transitions and order types in the random field O(N) model across dimensions, revealing the absence of certain phases in 3D.

Contribution

It provides a comprehensive phase diagram analysis of the random field O(N) model using nonperturbative FRG, highlighting the breakdown of dimensional reduction and the non-existence of QLRO in 3D.

Findings

Dimensional reduction breaks down below a critical line.

The phase diagram topology resembles the pure O(N) model.

Quasi-long range order is absent in 3D random field XY model.

Abstract

By applying the recently developed nonperturbative functional renormalization group (FRG) approach, we study the interplay between ferromagnetism, quasi-long range order (QLRO) and criticality in the $d$-dimensional random field O(N) model in the whole ($N$, $d$) diagram. Even though the "dimensional reduction" property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with however no equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that QLRO, namely a topologically ordered "Bragg glass" phase, is absent in the 3--dimensional random field XY model. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around $d=4$.