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Partition function zeros for the two-dimensional using model IV

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  • Stephenson, John

Abstract

The boundaries of regions containing complex temperature zeros of the partition function of the two-dimensional Ising model on completely anisotropic triangular and quadratic lattices are investigated in detail. Numerical solutions of the boundary equations are presented for triangular lattices with interactions in the ratios 3 : 2 : 1 and 4 : 2 : 1. For general anisotropic triangular and quadratic lattices, the origins of “pinch-points”, at which the boundary lines intersect, is elucidated, and the relation of critical and disorder points to pure imaginary zeros, and their role in the classification of zeros, is analyzed. An explanation is given of why interior (non-boundary) complex solutions of the critical point equations can occur for triangular lattices.

Suggested Citation

  • Stephenson, John, 1988. "Partition function zeros for the two-dimensional using model IV," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 148(1), pages 88-106.
    • Handle: RePEc:eee:phsmap:v:148:y:1988:i:1:p:88-106
    DOI: 10.1016/0378-4371(88)90136-7
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    1. Turnbull, Geoffrey K. & Niho, Yoshio, 1986. "The optimal property tax with mobile nonresidential capital," Journal of Public Economics, Elsevier, vol. 29(2), pages 223-239, March.
    2. Stephenson, John & Van Aalst, Jan, 1986. "Partition function zeros for the two-dimensional Ising model III," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 136(1), pages 160-175.
    3. Stephenson, John & Couzens, Rodney, 1984. "Partition function zeros for the two-dimensional Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 201-210.
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