Structure and motion of the Lee-Yang zeros

Hidetoshi Nishimori, Robert B. Griffiths

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


For an Ising model satisfying the Lee-Yang condition, the zeros of the partition function Z and those of the associated functions ZA in the space of imaginary magnetic fields at all lattice sites are determined by a single analytic hypersurface. The sense of motion of the zeros of Z as the interactions are varied can be related to the positions of the zeros of the ZA. Contrary to a plausible conjecture, it is not true that all of the zeros of Z in a uniform field tend towards the point ẑ = 1 in the complex fugacity plane as the temperature is lowered, but it is possible that the first zero (that nearest to ẑ = 1) has a monotone motion. Various simplicity and intertwining properties of the zeros of Z and ZA which generalize earlier results are proved by a new argument which makes direct use of the Lee-Yang property.

Original languageEnglish
Pages (from-to)2637-2647
Number of pages11
JournalJournal of Mathematical Physics
Issue number11
Publication statusPublished - 1982 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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