Partition Function Zeros Of The Square-Lattice Ising Model With Nearest- And Next-Nearest-Neighbor Interactions
PHYSICAL REVIEW E(2010)
摘要
The distributions of the partition function zeros in the complex a=e(2 beta J1) plane of the square-lattice Ising model with nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions are investigated as a function of R= J(2)/J(1). Starting from the well-known two-circle distribution of the zeros a = +/- 1 + root 2e(i theta) for R= 0, finally the partition function zeros lie on the unit circle a= e(i theta) for R=infinity. Between these two ends, the changes in the zero distributions are described. Using the partition function zeros, the critical point a(c)(R) and the thermal scaling exponent y(t)(R) are estimated for the Ising ferromagnet (equivalently, antiferromagnet) and superantiferromagnet. For the special case of R= 1/2, the possible implications of the zero distributions are also discussed.
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