Renormalization group transformations for spin systems

V. Kushnir*, Baruch Rosenstein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a systematic approach to perform real space renormalization group transformations of the "decimation type" using perturbation theory. This type of transformations beyond d = 1 is non-trivial even for the Gaussian model on the lattice. Such a transformation is constructed on a hypercubic lattice in arbitrary dimensions, and perturbation theory for spin models is developed around it. We check the formalism on the solvable O(N) symmetric Heisenberg chain. The decimations are especially useful to study models undergoing a continuous phase transition at zero temperature. Results for one class of such models, the D = 2 O(N) symmetric classical spins (N ≥ 3) for decimation with scale factor η = 2 (when one quarter of the points is left), are presented.

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Volume221
Issue number1-3
DOIs
StatePublished - 15 Nov 1995

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