Grassman path-integral solution for a class of triangular type decorated ising models

Abstract

Grassman path-integral solution is given for a class of two-dimensional triangular type decorated Ising models. Canonical Ising Lattices, rectangular, triangular and hexagonal, enter into this class as the most simple particular cases. As a first step, the problem is reformulated in terms of a free-fermionic field theory. The method is based on the mirror-factorization principle for the density matrix; traditional transfer-matrix or combinatorial considerations are not needed. The solution exhibits the characteristics free-fermionic structure providing the universal logarithmic singularity in the specific heat. The symmetries and the critical-point behaviour are investigated within the spin-polynomial interpretation of the problem. Some concrete decorated lattices are treated by illustration. Attention is given to the choice of rational computational devices.