Wilson's Theory of Critical Phenomena and Callan-Symanzik Equations in 4-ɛ Dimensions

The relevance of the Gell-Mann-Low eigenvalue condition to the description of the critical behavior in statistical mechanics is discussed in detail, using the natural framework of the Callan-Symanzik equations, in 4-ɛ dimensions. Wilson's method relying on the existence of a bare coupling constant adjusted to yield scaling laws in perturbation theory is justified and Wilson's results for critical exponents are rederived using renormalized perturbation theory.