# Novel effective ergodicity breaking phase transition in a driven-dissipative system

## TL;DR

This paper demonstrates a phase transition in a driven-dissipative system where ergodicity is broken, characterized by a change from uniform stress distribution to site-specific limit cycles, with evidence of critical scaling behavior.

## Contribution

It introduces a novel ergodicity breaking transition in the Olami-Feder-Christensen model driven by noise, using recurrence analysis to identify the transition's order parameter and critical exponents.

## Key findings

- Effective ergodicity breaking transition identified
- Recurrence rate used as order parameter
- Critical exponents suggest hyperscaling

## Abstract

We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the average stress on each site converges to the global average. Below the critical noise, the stress on individual sites becomes trapped in different limit cycles. We use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. We identify the order parameter as the recurrence rate averaged over all sites and find numerical evidence that the transition can be characterized by exponents that are consistent with hyperscaling.