# Fluctuation-dominated phase ordering at a mixed order transition

## TL;DR

This paper investigates a new type of order called fluctuation-dominated phase ordering that occurs along certain mixed order transition lines, characterized by large fluctuations and unique correlation function behavior.

## Contribution

It identifies and characterizes fluctuation-dominated phase ordering as a novel phenomenon occurring in mixed order transitions, supported by analysis of an Ising model with long-range interactions.

## Key findings

- Fluctuation-dominated order features large fluctuations in the thermodynamic limit.
- Correlation functions approach a finite value with a cusp singularity.
- Occurs along a portion of the transition line in a specific Ising model.

## Abstract

Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.