A numerical method to compute exactly the partition function with application to Z(n) theories in two dimensions

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Abstract

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for an n-state model on an Ldlattice scales like {Mathematical expression}. I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponents v and α and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.

Original languageEnglish (US)
Pages (from-to)55-75
Number of pages21
JournalJournal of Statistical Physics
Volume60
Issue number1-2
DOIs
StatePublished - Jul 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Potts and Ising models
  • exact partition function
  • exponents
  • scaling
  • zeros

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