We examine the percolation model by an approach involving lattice animals, divided according to their surface-area-to-volume ratio. Throughout, we work with the bond percolation model in Z. However, the results apply to the site or bond model on any infinite transitive amenable graph with inessential changes. For any given p ∈ (0, 1), two lattice animals with given size are equally likely to ar...

Starting from the Bethe ansatz solution we derive a set of coupled non-linear integral equations for the fully packed double loop model (FPL) on the square lattice. As an application we find exact expressions for the central charge and for the scaling dimension corresponding to the simplest charge excitation. We study numerically the low-lying excitations corresponding to more general perturbat...

All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using finite-size data of the type typically garnered from a computational approach. Here that method is extended to deal with more general cases. Other critical points of ...

Received by the editors on November 3, 2011. Accepted for publication on May 20, 2012. Handling Editor: Oskar Maria Baksalary. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187 USA ([email protected] and [email protected]). Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 25, pp. 72-83, Augus...

Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ/Γ0 is amenable. 0. Introduction and Results Let Γ be a group of isometries acting freely and properly discontinuously on a CAT(−1) space X . Roughly speaking, a CAT(−...

The solid–fluid phase transition of a granular material shaken horizontally is investigated numerically. We find that it is a first-order phase transition and propose two order parameters, namely the averaged kinetic energy and the averaged granular temperature, to determine the fluidization point precisely. It scales as amplitude times square of the frequency of the external vibration. Using t...

We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture resulting from our analysis allows us to characterize the large scale behavior of the present model with great accuracy. Sandpile automata [1] are prototypical mod...

The uniform model is a reversible interacting particle system that evolves on the homogeneous tree. Occupied sites become vacant at rate one provided the number of occupied neighbors does not exceed one. Vacant sites become occupied at rate times the number of occupied neighbors. On the binary tree, it has been shown that the survival threshold c is 1=4. In particular, for 1=4, the expected ext...

For all α ≥ RT (3) (where RT (3) = 7/4 is the repetition threshold for the 3-letter alphabet), there exists an infinite word over 3 letters whose critical exponent is α.

Based on the scaling relation for the dynamics at the early time, a new method is proposed to measure both the static and dynamic critical exponents. The method is applied to the two dimensional Ising model. The results are in good agreement with the existing results. Since the measurement is carried out in the initial stage of the relaxation process starting from independent initial configurat...