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

Flaviano Morone; Dries Sels

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arXiv · 2408.05339

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

Flaviano Morone·Dries Sels

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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.

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Flaviano Morone, Dries Sels. 2024-08-09. Re-entrant phase transitions induced by localization of zero-modes. https://arxiv.org/abs/2408.05339

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