Renormalization group maps for ising models in lattice-gas variables

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2 Scopus citations

Abstract

Real-space renormalization group maps, e.g., the majority rule transformation, map Ising-type models to Ising-type models on a coarser lattice. We show that each coefficient in the renormalized Hamiltonian in the lattice-gas variables depends on only a finite number of values of the renormalized Hamiltonian. We introduce a method which computes the values of the renormalized Hamiltonian with high accuracy and so computes the coefficients in the lattice-gas variables with high accuracy. For the critical nearest neighbor Ising model on the square lattice with the majority rule transformation, we compute over 1,000 different coefficients in the lattice-gas variable representation of the renormalized Hamiltonian and study the decay of these coefficients. We find that they decay exponentially in some sense but with a slow decay rate. We also show that the coefficients in the spin variables are sensitive to the truncation method used to compute them.

Original languageEnglish (US)
Pages (from-to)409-426
Number of pages18
JournalJournal of Statistical Physics
Volume140
Issue number3
DOIs
StatePublished - Jun 9 2010

Keywords

  • Ising model
  • Lattice gas variables
  • Majority rule
  • Renormalization group

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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