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We discuss the free-energy density of bosonic and fermionic theoriespossessing strongly coupled critical points in D=3. We construct a stationaryrenormalization group trajectory which interpolates between the free masslesstheory of N scalars and a class of interacting theories including both bosonsand fermions. At a special point of this trajectory the free-energy density is5/4 times the free-energy density of the O(N) vector model at its nontrivialcritical point. Our method could in principle be useful in the study of othertheories with strongly coupled fixed points, such as {\cal N}=4 SYM in D=4.Comment: 13 pages, RevTeX, 1 figure, version to appear in JHE

Stationary RG flow and thermodynamics of conformal field theories