Lee D-H, Wu F Y
Department of Physics, University of California, Berkeley, CA 94720, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 2):026111. doi: 10.1103/PhysRevE.67.026111. Epub 2003 Feb 13.
We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with some of its plaquettes frustrated has a dual model which is an Ising model with an external field ipi/2 applied to the dual sites centered at frustrated plaquettes. In the case where all plaquettes are frustrated, this leads to the known result that the dual model has a uniform field ipi/2, whose partition function can be evaluated in the thermodynamic limit for regular lattices. The analysis is extended to a Potts spin glass with analogous results obtained.
我们考虑具有受挫相互作用的任意平面图和晶格上的离散自旋模型。我们首先分析具有受挫格点的伊辛模型。我们使用代数方法得出结果，即其一些格点受挫的伊辛模型有一个对偶模型，该对偶模型是一个在以受挫格点为中心的对偶格点上施加了外场(\pi/2)的伊辛模型。在所有格点都受挫的情况下，这导致了已知结果，即对偶模型有一个均匀场(\pi/2)，其配分函数在规则晶格的热力学极限下可以计算。该分析扩展到具有类似结果的Potts自旋玻璃。
