Scaling theory of thermal rounding phenomena in depinning and related transitions

TL;DR

This paper develops a scaling theory to describe how thermal fluctuations smooth out the sharp depinning transition and related phenomena, providing predictions for the thermal rounding exponent and insights into correlations of activated events.

Contribution

It introduces a novel scaling framework for thermal rounding in depinning and directed percolation, predicting the thermal rounding exponent and analyzing correlations.

Findings

Predicts the thermal rounding exponent for depinning transitions

Provides a scaling description of thermal effects on transition sharpness

Analyzes non-trivial spatial and temporal correlations of activated events

Abstract

We present a scaling theory for the effect of thermal fluctuations on the characteristics of the depinning transition, and also in the closely related directed percolation model. Thermal effects act as a sort of external field that produces a rounding of the sharp transition occurring at zero temperature. The theory allows to predict the value of the thermal rounding exponent that quantifies the rounding effect. It also gives insight into the spatial and temporal correlations between thermally activated events, which are highly non-trivial.