COMPUTATION OF HIERARCHICAL RENORMALIZATION-GROUP FIXED-POINTS AND THEIR EPSILON-EXPANSIONS

We compute hierarchical renormalization-group fixed points as solution s to an algebraic equation for the coupling constants. This method doe s not rely on an iteration of renormalization-group transformations an d therefore avoids the problem of fine tuning. We solve truncated vers ions of the fixed-point equation numerically for different values of t he dimension parameter in the range 2 < d < 4 and different orders of truncations. The method is well suited even for multicritical fixed po ints with any number of unstable directions. Precise numerical data ar e presented for the first three nontrivial fixed points and their crit ical indices. We also develop an epsilon-expansion for the hierarchica l models using computer algebra. The numerical results are compared wi th the epsilon-expansion.