Minimal renormalization without ε expansion: Four-loop free energy in three dimensions for general n above and below Tc

We present an analytic four-loop calculation of the free energy in three dimensions within the O(n) symmetric φ4 theory at infinite cutoff for general n above and below Tc. It is shown that Goldstone singularities arising at intermediate stages of the calculation cancel among themselves. The correlation length above Tc and an appropriately defined pseudocorrelation length below Tc are calculated analytically up to four-loop order for general n. The method of minimal renormalization at fixed dimension d=3 is used to determine the analytic expressions for the four-loop series of the amplitude functions of the free energy, correlation length, and specific heat above and below Tc in terms of the renormalized coupling. These expressions provide the basis for future accurate Borel resummations of universal amplitude ratios characterizing the asymptotic critical behavior and of crossover functions describing the nonasymptotic critical behavior. A brief application is given by a variational calculation of the universal specific-heat amplitude ratios A+/A- and P=α-1(1-A+/A-) and of the universal quantity Rξ+=ξ0+(A+)1/d for general n