Complex-temperature singularities of the susceptibility in the D=2 Ising model. I. Square lattice

V. Matveev, R. Shrock

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We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that, as one approaches the point u=u s=-1 (where u=e'4K) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form X approximately As'(1+u)(- gamma s') with exponent gamma s'=3/2. The critical amplitude As' is calculated. Other critical exponents are found to be alpha s'= sigma s=0 and beta s= 1/4 , so that the scaling relation alpha s'+2 beta s+ gamma s' is satisfied. However, using exact results for beta s on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: beta s is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point u=-1 from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.

Original languageEnglish (US)
Article number012
Pages (from-to)1557-1583
Number of pages27
JournalJournal of Physics A: Mathematical and General
Issue number6
StatePublished - 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


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