Screened perturbation theory to three loops

The thermal physics of a massless scalar field with a ${\phi }^4$ interaction is studied within screened perturbation theory (SPT). In this method the perturbative expansion is reorganized by adding and subtracting a mass term in the Lagrangian. We consider several different mass prescriptions that generalize the one-loop gap equation to two-loop order. We calculate the pressure and entropy to three-loop order and the screening mass to two-loop order. In contrast with the weak-coupling expansion, the SPT-improved approximations appear to converge even for rather large values of the coupling constant.