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Recently, non-perturbative approximate solutions were presented that gobeyond the well-known mean-field resummation. In this work, thesenon-perturbative approximations are used to calculate finite temperatureequilibrium properties for scalar $\phi^4$ theory in two dimensions such as thepressure, entropy density and speed of sound. Unlike traditional approaches, itis found that results are well-behaved for arbitrary temperature/couplingstrength, are independent of the choice of the renormalization scale$\bar\mu^2$, and are apparently converging as the resummation level isincreased. Results also suggest the presence of a possible analytic cross-overfrom the high-temperature to the low-temperature regime based on the change inthe thermal entropy density.

Simple non-perturbative resummation schemes beyond mean-field II: thermodynamics of scalar $\phi^4$ theory in 1+1 dimensions at arbitrary coupling