ϕ34lattice field theory viewed from the high-temperature side

Abstract

We analyze high-temperature series expansions of the two- and four-point correlation functions in the three-dimensional Euclidean lattice scalar field theory with quartic self-coupling, which have been recently extended through 25th order for the simple-cubic and body-centered-cubic lattices. We conclude that the length of the present series is sufficient for a fairly accurate description of the critical behavior of the model and confirm the validity of universality, scaling, and hyperscaling. In the case of the body-centered-cubic lattice, we determine the value of the quartic self-coupling for which the leading corrections to scaling approximately vanish and correspondingly the universal critical parameters can be determined with high accuracy. In particular, for the susceptibility and the correlation-length exponents we find $\ensuremath{\gamma}=1.2373(2)$ and $\ensuremath{\nu}=0.6301(2)$. For the four-point renormalized coupling we find $g=23.56(3)$. In the case of the simple-cubic lattice our results are consistent with earlier estimates.