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Renormalization group approach as an approximate solution of diophantine system of equations: Application to the Ising model

✍ Scribed by Savely Rabinovich

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 268 KB
Volume: 230
Category: Article
ISSN: 0378-4371
DOI: 10.1016/0378-4371(96)00061-1

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✦ Synopsis

It is demonstrated that the real-space renormalization group approach is equivalent to an appropriate diophantine system of equations. The method is applied on several examples of the Ising model.

There exist many papers and books concerning with different aspects of renormalization group (RG) approach (see e.g. ). This paper deals with one of the topics that still remains uncovered, namely, RG of microcanonical partition function and its number-theoretical meaning.

The method presented here will be demonstrated in detail on the simplest Ising model and then generalized for more complicated cases.

A partition function for the 1D Ising model reads

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