The percolation transition in the zero-temperature Domany model

Research output: Contribution to journalArticle

Abstract

We analyze a deter ministic cellular automaton σ = (σn.: n ≥ 0) corresponding to the zero temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice ℍ The state space script capital L signℍ = {-1, +1} consists of assignments of -1 or +1 to each site of ℍ and the initial state σ0 = {σx 0} x ∈ ℍ is chosen randomly with P(σx 0 = +1) p ∈ [0, 1]. The sites of ℍ are partitioned in two sets script A sign and ℬ so that all the neighbors of a site in script A sign belong to ℬ and vice versa, and the discrete time dynamics is such that the σx .'s with x ∈ script A sign (respectively, ℬ) are updated simultaneously at odd (resp, even) times, making σx . agree with the majority of its three neighbors. In ref. 1 it was proved that there is a percolation transition at p = 1/2 in the percolation models defined by σn, for all times n ∈ [1, ∞]. In this paper, we study the nature of that transition and prove that the critical exponents β, ν, and η of the dependent percolation models defined by σn, n ∈ [1, ∞], have the same values as for standard two dimensional independent site percolation (on the triangular lattice).

Original languageEnglish (US)
Pages (from-to)1199-1210
Number of pages12
JournalJournal of Statistical Physics
Volume114
Issue number5-6
Publication statusPublished - Mar 2004

    Fingerprint

Keywords

  • Cellular automaton
  • Critical exponents
  • Dependent percolation
  • University
  • Zero-temperature dynamics

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this