Exactly Soluble Models

  • Giovanni Gallavotti
Part of the Texts and Monographs in Physics book series (TMP)


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.


Partition Function Ising Model Transfer Matrix Pair Correlation Function Heisenberg Model 
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  1. 3.
    Because as mentioned above their statistical mechanics properties are quite normal, as shown in [LW72], p. 354–361.Google Scholar
  2. 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

Authors and Affiliations

  • Giovanni Gallavotti
    • 1
  1. 1.Dipartimento di FisicaUniversità degli Studi di Roma “La Sapienza”RomaItaly

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