Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice

P. D. Alvarez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.

Original languageEnglish
Article number083101
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2024
Issue number8
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 IOP Publishing Ltd and SISSA Medialab srl.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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