General Relation between the Specific Heat above and below a Second-Order Phase Transition

A general relation between the critical specific heat above and below a second-order phase transition is derived. It is expressed in terms of the effective four-point coupling $u\left(l\right)\mathrm{}$ of the Ginzburg-Landau Hamiltonian and is valid in the entire region between asymptotic criticality and noncritical background behavior. Application to the $\lambda$ transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ yields excellent agreement with the fixed-point value $u^{*}=u\left(0\right)\mathrm{}$ predicted by high-order perturbation theory.