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

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).

arXiv comment22 pages and 20 figures

References in corpus (8)

• W-symmetry in Conformal Field Theory
• The abelian sandpile and related models
• Conformal Field Theories of Stochastic Loewner Evolutions
• Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• The raise and peel model of a fluctuating interface
• Stochastic processes and conformal invariance
• NUMERICAL INVESTIGATION OF CORRELATION FUNCTIONS FOR THE U_qSU(2) INVARIANT SPIN-1/2 HEISENBERG CHAIN

Cited by in corpus (6)

• Shared Information in Stationary States at Criticality
• Different facets of the raise and peel model
• Density profiles in the raise and peel model with and without a wall. Physics and combinatorics
• Critical phases in the raise and peel model
• Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
• Avalanches in the Raise and Peel model in the presence of a wall