Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre Avalanches in the raise and peel model in the presence of a wall. (English) Zbl 1271.82016 J. Phys. A, Math. Theor. 46, No. 26, Article ID 265001, 15 p. (2013). 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) Keywords:raise and peel model; Monte Carlo simulations; XXZ quantum chain; conformal field theory; Markov process PDFBibTeX XMLCite \textit{E. Antillon} et al., J. Phys. A, Math. Theor. 46, No. 26, Article ID 265001, 15 p. (2013; Zbl 1271.82016) Full Text: DOI arXiv