Renormalization group approach to the spin-1 Bose gas

TL;DR

This paper uses a two-loop renormalization group approach to analyze the phase transition nature in homogeneous spin-1 Bose gases, revealing a first-order transition for weak spin-dependent couplings.

Contribution

It applies a detailed two-loop renormalization group analysis to determine the order of phase transitions in spin-1 Bose gases, extending previous studies with higher-order calculations.

Findings

Phase transition is first order for weak spin-dependent couplings.

Beta functions are computed up to third order in coupling constants.

Free energy near stability border is derived in next-to-leading order.

Abstract

A field theoretical renormalization group approach at two loop level is applied to the homogeneous spin-1 Bose gas in order to investigate the order of the phase transition. The beta function of the system with $d=4-\epsilon$ dimensions is determined up to the third power of the coupling constants and the system's free energy on the border of the classical stability is given in next to leading order. It is found that the phase transition of the interacting spin-1 Bose gases with weak spin-dependent coupling constant values is of first order.