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Avalanches in the raise and peel model in the presence of a wall. (English) Zbl 1271.82016

Summary: We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of the adsorption (\(u_a\)) and desorption (\(u_d\)) rates, the model shows interesting features. At \(u_a = u_d\), the model is described by a conformal field theory (with conformal charge \(c=0\)), and its stationary probability can be mapped onto the ground state of the XXZ quantum chain. Moreover, for the regime \(u_a\geqslant u_d\), the model shows a phase in which the avalanche distribution is scale-invariant.
In this work, we study the surface dynamics by looking at avalanche distributions using a finite-sized scaling formalism and explore the effect of adding a wall to the model. The model shows the same universality for the cases with and without a wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of tiles released in an avalanche. New insights into the effect of parity on avalanche distributions are discussed, and we provide a new conjecture for the probability distribution of avalanches with a wall obtained by using an exact diagonalization of small lattices and Monte Carlo simulations.

MSC:

82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
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