# Large deviations in models of growing clusters with symmetry-breaking transitions

## TL;DR

This paper investigates large deviations of magnetisation in models of growing clusters with symmetry-breaking transitions, revealing unexpected power-law decay of certain fluctuations and their relation to dynamical phase coexistence.

## Contribution

It demonstrates that the rate function is zero for intermediate magnetisation values, leading to power-law decay of fluctuations, a novel insight into large deviations in such models.

## Key findings

- Power-law decay of magnetisation fluctuations
- Rate function is zero for intermediate magnetisation
- Connection to dynamical phase coexistence phenomena

## Abstract

We analyse large deviations of the magnetisation in two models of growing clusters. The models have symmetry-breaking transitions, so the typical magnetisation of a growing cluster may be either positive or negative, with equal probability. For large clusters, the magnetisation obeys a large deviation principle. We show that the corresponding rate function is zero for values of the magnetisation that are intermediate between the two steady state values, which means that fluctuations with these values of the magnetisation are much less unlikely than previously thought. We show that their probabilities decay as power laws in the cluster size, instead of the exponential scaling that would be expected from the large deviation principle. We discuss how this observation is related to dynamical phase coexistence phenomena. We also comment on the typical size of magnetisation fluctuations.