Decimation in more then one dimension

Details Decimation in more then one dimension Decimation in more then one dimension

1995-05-29

arxiv.org/abs/cond-mat/9505144v1

Phys.Lett. B357 (1995) 169-176

Physics

Condensed Matter

17 pages, latex, 3 diagrams using FEYNMAN

Scientific paper

10.1016/0370-2693(95)00876-M

We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism on solvable case of $O(N)$ symmetric Heisenberg chain. The transformation is particularly useful to study asymptotically free theories. Results for one class of such models, the d=2 O(N) symmetric $\sigma$ models ($N\ge 3$) for decimation with scale factor $\eta=2$ (when quarter of the points is left) are given as an example.

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