TY - JOUR

T1 - Structure and motion of the Lee-Yang zeros

AU - Nishimori, Hidetoshi

AU - Griffiths, Robert B.

PY - 1982/12/1

Y1 - 1982/12/1

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:7544225360

VL - 24

SP - 2637

EP - 2647

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

ER -