Landau theory of bi-criticality in a random quantum rotor system

TL;DR

This paper develops a Landau theory for a generalized random quantum rotor model with non-zero mean interactions, revealing phase transitions, the Gabay-Toulouse line, and replica symmetry breaking, with results matching experimental observations.

Contribution

It introduces a Landau theoretical framework for a generalized quantum rotor system with non-zero mean interactions, including ferromagnetic and superconducting phases, and analyzes phase transitions and symmetry breaking.

Findings

Existence of a Gabay-Toulouse line for M>1.

All phase transitions are second order.

Phase diagram features match experimental data for LiHo_xY_{1-x}F_4.

Abstract

We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of non-zero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange interactions has non-zero mean. The solution to the saddle point equations is presented in the vicinity of the bi-critical point characterized by the intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the paramagnetic and spin glass phases. All transitions are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is non-analytic in the parameter that controls the paramagnet/ferromagnet transition in the absence of disorder. Also for M=1, we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for M=1, are {\it identical} to what is observed experimentally in the random magnetic alloy $LiHo_xY_{1-x}F_4$.