High temperature critical O(N) field models by LCE series

TL;DR

This paper uses high-order linked cluster series to analyze the critical properties of O(N) field models at high temperatures, revealing their weak coupling nature and matching critical exponents with 3D superrenormalizable models.

Contribution

It introduces a method using high-order linked cluster series to determine critical properties of renormalizable O(N) models at finite temperature.

Findings

Models become weakly coupled at phase transition

Critical exponents match those of 3D superrenormalizable models

Renormalizable couplings induce measurable corrections

Abstract

The critical properties of renormalizable O(N) field models are determined by means of the high order ($\geq 18$) behaviour of convergent linked cluster series on finite temperature lattices. It is shown that those models become weakly coupled at the phase transition. The critical exponents agree to those of the corresponding superrenormalizable 3-dimensional models. Concerning critical amplitudes and subcritical behaviour, corrections induced by renormalizable couplings are measurable.