Conformal invariance and its breaking in a stochastic model of a fluctuating interface

TL;DR

This study uses Monte Carlo simulations to explore how a parameter affects a stochastic model of a fluctuating interface, revealing a transition from conformal invariance to its breaking and continuous variation of critical exponents.

Contribution

It provides the first example of a system exhibiting a phase with scale invariance but broken conformal invariance, with continuously varying critical exponents.

Findings

System is massive for 0<u<1

System is conformal invariant at u=1

Conformal invariance is broken for u>1

Abstract

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter $u$ (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for $0<u<1$ the system is massive, for $u=1$ it is massless and conformal invariant. For $u>1$ the conformal invariance is broken. The system is in a scale invariant but not conformal invariant phase. As far as we know it is the first example of a system which shows such a behavior. Moreover in the broken phase, the critical exponents vary continuously with the parameter $u$. This stays true also for the critical exponent $\tau$ which characterizes the probability distribution function of avalanches (the critical exponent $D$ staying unchanged).