Algebraic Computation of the Hierarchical Renormalization Group Fixed Points and their $\epsilon$-Expansions

Abstract

Nontrivial fixed points of the hierarchical renormalization group are computed by numerically solving a system of quadratic equations for the coupling constants. This approach avoids a fine tuning of relevant parameters. We study the eigenvalues of the renormalization group transformation, linearized around the non-trivial fixed points. The numerical results are compared with $\epsilon$-expansion.

LaTex file, 24 pages, 5 figures appended as 1 PostScript file, preprint MS-TPI-94-2

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