Exact partition functions of the Ising model on M × N planar lattices with periodic-aperiodic boundary conditions

Ming Chya Wu, Chin Kun Hu

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on M × N square (sq), plane triangular (pt) and honeycomb (he) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/kB, as a function of temperature, θ = kBT/J. We find that for the N × N sq lattice, C/kB for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N × W pt and he lattices, C/kB for ap, pa and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model.

Original languageEnglish
Pages (from-to)5189-5206
Number of pages18
JournalJournal of Physics A: Mathematical and General
Volume35
Issue number25
DOIs
StatePublished - 28 Jun 2002

Fingerprint

Dive into the research topics of 'Exact partition functions of the Ising model on M × N planar lattices with periodic-aperiodic boundary conditions'. Together they form a unique fingerprint.

Cite this