Exactly Soluble Models

Abstract

Many well-known exact solutions of statistical mechanical models are based on the transfer matrix method. In fact the summation over the states of the system, e.g. the sum over the values of the spin at each site, can be quite easily interpreted as an operation of summing over the labels of a product of matrices in order to compute the trace of the product. Thus the problem of computing, say, a partition function is “reduced” to that of diagonalizing certain matrices with the purpose of computing their eigenvalues and eigenvectors. The latter sometimes also provide informations on the correlation functions.