Green's function theory for the Cheng–Schick model of 3He–4He mixtures

Abstract

In this paper, we outline a theory for the thermodynamic properties of 3 He –4 He mixtures in the neighborhood of the critical line and the tricritical point (TCP). The theory utilizes the Cheng–Schick (CS) lattice gas model where both the 3 He and 4 He atoms are treated as quantum particles on a lattice. The analysis is based on Green's function approach. Results are presented for the ordering susceptibility and the thermal averages of the occupation numbers of 3 He and 4 He atoms. We derive a self-consistent equation for the ordering susceptibility and use it to calculate the critical line and locate the TCP. Our findings are compared with the predictions obtained from high temperature series expansions, mean field theory and the random phase approximation (RPA).