Wilson's Theory of Critical Phenomena and Callan-Symanzik Equations in4−εDimensions

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 $4-\epsilon$ 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.