10
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)

      Preprint
      , ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter \(\kappa = 2\). In this paper we consider the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation. We examine the scaling behavior of a number of functions such as the correlation length, the exponent of distribution function of loop lengths and gyration radius defined for waves and avalanches. We find that they do scale with the rate of dissipation. Two significant length scales are observed. For length scales much smaller than the correlation length, these curves show properties close to the critical curves and the corresponding diffusivity parameter is nearly the same as the critical limit. We interpret this as the ultra violet (UV) limit where \(\kappa = 2\) corresponding to \(c=-2\). For length scales much larger than the correlation length we find that the avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving function is proportional to the Brownian motion with the diffusion parameter \(\kappa =8/3\) corresponding to a field theory with \(c = 0\). This is the infra red (IR) limit. Correspondingly the central charge decreases from the IR to the UV point.

          Related collections

          Most cited references6

          • Record: found
          • Abstract: not found
          • Article: not found

          Phase organization

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Exact fractal dimension of the loop-erased self-avoiding walk in two dimensions.

            (1992)
              Bookmark
              • Record: found
              • Abstract: found
              • Article: found
              Is Open Access

              Scaling fields in the two-dimensional abelian sandpile model

              We consider the isotropic two-dimensional abelian sandpile model from a perspective based on two-dimensional (conformal) field theory. We compute lattice correlation functions for various cluster variables (at and off criticality), from which we infer the field-theoretic description in the scaling limit. We find a perfect agreement with the predictions of a c=-2 conformal field theory and its massive perturbation, thereby providing direct evidence for conformal invariance and more generally for a description in terms of a local field theory. The question of the height 2 variable is also addressed, with however no definite conclusion yet.
                Bookmark

                Author and article information

                Journal
                08 February 2012
                Article
                10.1103/PhysRevE.85.051104
                1202.1658
                f64fabc0-d953-4751-b3a0-7638c629772e

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                11 Pages, 6 Figures
                cond-mat.stat-mech

                Comments

                Comment on this article