Spontaneous magnetization of quantum $XY$ spin model in joint presence of quenched and annealed disorder

TL;DR

This paper studies how quenched and annealed disorder affect spontaneous magnetization in the quantum XY spin-1/2 model, revealing conditions where disorder does not influence critical temperature or magnetization.

Contribution

It provides a comparative analysis of quenched and annealed disorder effects on magnetization and critical temperature in the quantum XY model within a mean-field framework.

Findings

Critical temperature for magnetization in the field direction is unaffected when interaction is quenched and field is annealed.

Annealed disorder in interactions does not alter magnetization or critical temperature.

Disorder type and placement significantly influence the magnetic properties of the system.

Abstract

We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or/and annealed disorder. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales - the time scale associated with the equilibriation of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We observe in particular that when interaction and field terms are respectively quenched and annealed, critical temperature for the system to magnetize in the direction parallel to the applied field does not depend on any of the disorders. Further, an annealed disordered interaction neither affects the magnetizations nor the critical temperatures. We carry out a comparative study of the different combinations of the disorders in the interaction and field terms, and point out their generic features.