Mass expansions of screened perturbation theory

The thermodynamics of massless φ⁴ theory 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 analytically calculate the pressure and entropy to three-loop order and the screening mass to two-loop order, expanding in powers of $m/T.$ The truncated $m/T$ expansion results are compared with numerical SPT results for the pressure, entropy and screening mass which are accurate to all orders in $m/T.$ It is shown that the $m/T$ expansion converges quickly and provides an accurate description of the thermodynamic functions for large values of the coupling constant.