Complex-temperature properties of the two-dimensional Ising model for nonzero magnetic field

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 1, 1996, Pages 254-267

  Matveev, Victor ^a   Shrock, Robert ^a  

^a STONY BROOK UNIVERSITY   (United States)

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EID: 4243900846     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.254     Document Type: Article

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40. Parenthetically, we note that for anisotropic spin spin couplings, the complex temperature zeros would merge to form areas instead of curves in the thermodynamic limit Ref. 22. Indeed, for the (heteropolygonal) 4 ×82 lattice, even if the couplings are isotropic, the zeros still form areas in this limit Ref. 23.
41. To save space, we truncate the plot on the left at Re(u)=-2; there are four zeros lying on the negative real axis, and a pair lying near this axis, to the left of this point, which are not shown. However, the plot as shown contains all the information, since these six zeros are just the inverses, by the u to 1/u symmetry, of the six which are shown, lying on or near the negative real axis within the unit circle.
42. As discussed in Ref. 19, in addition to this additive term there is also a subdominant contribution to the singularity in f at u=1 arising from the vanishing of the argument of the logarithm in Eq. (2.29) of that paper.