Complex-temperature properties of the Ising model on 2D heteropolygonal lattices

V. Matveev, R. Shrock

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, ( (kagome), (3.122) and (4.82) (bathroom tile), where the notation denotes the regular n-sided polygons adjacent to each vertex. We also work out the exact complex-temperature singularities of the spontaneous magnetization. A comparison with the properties on the square, triangular, and hexagonal lattices is given. In particular, we find the first case where, even for isotropic spin-spin exchange couplings, the non-trivial non-analyticities of the free energy of the Ising model lie in a two-dimensional, rather than one-dimensional, algebraic variety in the z=e-2K plane.

Original languageEnglish (US)
Article number014
Pages (from-to)5235-5256
Number of pages22
JournalJournal of Physics A: General Physics
Issue number18
StatePublished - 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


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