Chang SC, Shrock R
C. N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794-3840, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Oct;62(4 Pt A):4650-64. doi: 10.1103/physreve.62.4650.
We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L(y)=3 and L(y)=4 vertices and arbitrarily great length Lx vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the Lx-->infinity limits of the strips that we study. With the generalization of q from Z+ to C, we determine the analytic structure of W(q) in the q plane for the various cases.
我们给出了在具有次近邻自旋 - 自旋耦合的q态Potts反铁磁体的零温度配分函数（色多项式）和基态熵的指数W(q)的精确计算结果。该反铁磁体位于宽度为L(y)=3和L(y)=4个顶点且长度Lx任意大的方形晶格条带上，同时考虑了自由边界条件和周期性边界条件。将一系列物理q值下得到的W值相互比较，并与完整二维晶格的值进行比较。这些结果有助于深入了解此类非近邻耦合对基态熵的影响。我们表明，在我们所研究的条带的Lx→∞极限下，q = 2（伊辛）和q = 4的Potts反铁磁体具有零温度临界点。通过将q从正整数推广到复数，我们确定了各种情况下W(q)在q平面中的解析结构。
