Effective Critical Exponents from Finite Temperature Renormalization Group
Abstract
Effective critical exponents for the λ φ4 scalar field theory are calculated as a function of the renormalization group block size ko-1 and inverse critical temperature βc. Exact renormalization group equations are presented up to first order in the derivative expansion and numerical solutions are obtained with and without polynomial expansion of the blocked potential. For a finite temperature system in d dimensions, it is shown that βc = βc ko determines whether the d-dimensional (βc << 1) or (d+1)-dimensional (βc >> 1) fixed point governs the phase transition. The validity of a polynomial expansion of the blocked potential near criticality is also addressed.
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