Statistical Mechanics pp 209-231 | Cite as

# Exactly Soluble Models

Chapter

## 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.

## Keywords

Partition Function Ising Model Transfer Matrix Pair Correlation Function Heisenberg Model
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## References

- 3.Because as mentioned above their statistical mechanics properties are quite normal, as shown in [LW72], p. 354–361.Google Scholar
- 4.This was important progress as it provided a simple and easily understandable entirely new approach to the solution of the Ising model, at a time when it rested on the original works [On44] ,[Ka49] , [Ya52] which were still considered very hard to follow in the 1960s.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1999