Mathematical properties of renormalization-group transformations

Robert B. Griffiths

Physica A: Statistical Mechanics and its Applications, 1981, vol. 106, issue 1, 59-69

Abstract: Renormalization-group transformations of the type introduced into statistical physics by K. G. Wilson have been widely used with great success for a variety of many-body calculations. The basic approach consists in integrating out certain degrees of freedom and using a new “image” Hamiltonian to describe the statistical properties of those that remain. The mathematical foundations of the procedure, however, remain somewhat obscure. P.A. Pearce and the author have pointed out that there are serious questions about the existence and properties of a thermodynamic limit for renormalization-group transformations. In particular, certain real-space transformations show peculiarities in this limit. These suggest that there may be serious mathematical problems with renormalization-group procedures, despite their considerable practical sucess.

Date: 1981
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437181902065
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:106:y:1981:i:1:p:59-69

DOI: 10.1016/0378-4371(81)90206-5

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().