Re-entrant phase transitions induced by localization of zero-modes

TL;DR

This paper introduces a universal microscopic theory explaining re-entrant phase transitions caused by zero-mode localization, showing how disorder-induced localization leads to loss of long-range order in inhomogeneous systems.

Contribution

It proposes a universal microscopic mechanism for re-entrant phase transitions based on zero-mode localization, applicable across various inhomogeneous systems.

Findings

Predicts two critical temperatures in inhomogeneous systems.

Shows zero-mode localization causes loss of long-range order.

Explains the ubiquity of re-entrant phase transitions.

Abstract

Common wisdom dictates that physical systems become less ordered when heated to higher temperature. However, several systems display the opposite phenomenon and move to a more ordered state upon heating, e.g. at low temperature piezoelectric quartz is paraelectric and it only becomes piezoelectric when heated to sufficiently high temperature. The presence, or better, the re-entrance of unordered phases at low temperature is more prevalent than one might think. Although specific models have been developed to understand the phenomenon in specific systems, a universal explanation is lacking. Here we propose a universal simple microscopic theory which predicts the existence of two critical temperatures in inhomogeneous systems, where the lower one marks the re-entrance into the less ordered phase. We show that the re-entrant phase transition is caused by disorder-induced spatial localization of the zero-mode on a finite, i.e. sub-extensive, region of the system. Specifically, this trapping of the zero-mode disconnects the fluctuations of the order parameter in distant regions of the system, thus triggering the loss of long-range order and the re-entrance into the disordered phase. This makes the phenomenon quite universal and robust to the underlying details of the model, and explains its ubiquitous observation.