### Abstract

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 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} 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.

Original language | English |
---|---|

Article number | 265001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 26 |

DOIs | |

Publication status | Published - 5 Jul 2013 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*46*(26), [265001]. https://doi.org/10.1088/1751-8113/46/26/265001

**Avalanches in the raise and peel model in the presence of a wall.** / Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 46, no. 26, 265001. https://doi.org/10.1088/1751-8113/46/26/265001

}

TY - JOUR

T1 - Avalanches in the raise and peel model in the presence of a wall

AU - Antillon, Edwin

AU - Wehefritz-Kaufmann, Birgit

AU - Kais, Sabre

PY - 2013/7/5

Y1 - 2013/7/5

N2 - 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 adsorption (ua) and desorption (ud) rates, the model shows interesting features. At ua = ud, 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 ua ud, 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.

AB - 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 adsorption (ua) and desorption (ud) rates, the model shows interesting features. At ua = ud, 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 ua ud, 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.

UR - http://www.scopus.com/inward/record.url?scp=84879336547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879336547&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/26/265001

DO - 10.1088/1751-8113/46/26/265001

M3 - Article

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 26

M1 - 265001

ER -