Gaussian-to-Heisenberg crossover behavior of the specific heat in renormalized perturbation theory

A cutoff-dependent formulation of renormalized perturbation theory is used to study the Gaussian-to-Heisenberg crossover, describing the changeover from tricritical to critical-line behavior, for the specific heat, to second order in ε=4-d, in extension of earlier work by Bruce and Wallace for the susceptibility. The role of the nonhomogeneous part of the renormalization-group equation for the bare vertex function Γ(2,0) - proportional to the specific heat - with two φ² insertions is discussed in detail in an isotropic φ⁴ field model. An explicit crossover scaling function for the specific heat is calculated and the effective exponent αeff is found to differ considerably from an earlier first-order calculation.