Critical Exponents Below Tc Via Skeleton Graphs (Ising-Like Case)
We will discuss a method of calculating critical exponents in d = 4 – ɛ dimensions below the critical point. Although for T < Tc it is easy to obtain the 0(ɛ) corrections to the Gaussian model by several different approaches1, 2 and very laborious to generate exponents to 0(ɛ2) by any method, we will discuss here only the former case for a one-component classical field (“Ising-like”), our wish being to illustrate how one can use the method of “skeleton graphs” (or in the language of field theory, “fully-renormalized perturbation theory”) to generate critical exponents as a power series in ɛ in the presence of a broken symmetry. We will also show in a transparent way precisely which assumptions lead to Widom’s scaling form of the equation of state and to certain scaling laws for exponents for T < Tc.
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