Critical behavior in a non-local interface model

TL;DR

This paper investigates the phase transition and spectral properties of the non-local Raise and Peel interface model, combining exact diagonalization and Monte Carlo methods to analyze its critical behavior.

Contribution

It provides new insights into the phase diagram and scaling properties of the model away from the critical point, where they were previously unknown.

Findings

Spectral gap analysis indicates possible phase transition points.

Monte Carlo simulations reveal scaling behavior of observables.

Exact diagonalization results support the existence of critical phenomena.

Abstract

The Raise and Peel model is a recently proposed one-dimensional statistical model describing a fluctuating interface. The evolution of the model follows from the competition between adsorption and desorption processes. The model is non-local due to the possible occurrence of avalanches. At a special ratio of the adsorption-desorption rates the model is integrable and many rigorous results are known. Off the critical point, the phase diagram and scaling properties are not known. In this paper, we search for indications of phase transition studying the gap in the spectrum of the non-hermitian generator of the stochastic interface evolution. We present results for the gap obtained from exact diagonalization and from Monte Carlo estimates derived from temporal correlations of various observables.