The raise and peel model of a fluctuating interface

Abstract

We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is given by conformal field theory, and the stationary non-equilibrium probability distribution is given by the two-dimensional equilibrium distribution of the ice model with domain wall type boundary conditions. This connection is used to find exact analytic expressions for several quantities of the stochastic model. Vice versa, some understanding of the ice model with domain wall type boundary conditions can be obtained by the study of the stochastic model. At the special point we study several properties of the model, such as the height fluctuations as well as cluster and avalanche distributions. The latter has a long tail which shows that the model exhibits self organized criticality. We also find in the stationary state a special phase transition without enhancement and with a crossover exponent $\varphi =2/3$. Furthermore, we study the phase diagram of the model as a function of the adsorption rate and find two massive phases and a scale invariant phase where conformal invariance is broken.

LaTeX, 34 pages, 23 Postscript figures

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• From boundary to bulk in logarithmic CFT
• Logarithmic torus amplitudes
• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• The two-boundary Temperley-Lieb algebra
• The logarithmic triplet theory with boundary
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
• Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
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• Exact results for an asymmetric annihilation process with open boundaries
• Wind on the boundary for the Abelian sandpile model
• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• Conformal invariance and its breaking in a stochastic model of a fluctuating interface
• Shared Information in Stationary States at Criticality
• Nonlocal Asymmetric exclusion process on a ring and conformal invariance
• The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance
• Different facets of the raise and peel model
• Correlation functions in conformal invariant stochastic processes
• The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics
• Phase diagram and spectral properties of a new exactly integrable spin one quantum chain
• Supersymmetric Model of Spin-1/2 Fermions on a Chain
• Refined Razumov-Stroganov conjectures for open boundaries
• From conformal invariance to quasistationary states
• A conformal invariant growth model
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• Laws of large numbers in the Raise and Peel model
• Critical phases in the raise and peel model
• Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
• Large deviations of avalanches in the raise and peel model
• Avalanches in the Raise and Peel model in the presence of a wall
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field
• Critical behavior in a non-local interface model