Abstract

We describe recent work3 on the equilibrium thermodynamics of a lattice boson gas, in three dimensions, with the onsite repulsion and nearest neighbor sites atraction. For this system the existence of Bose — condensation is proven and an equation for the critical temperature is obtained. Moreover, upper and lower bounds for the static structure factor are derived. In this work we also study the equilibrium thermodynamics of the mean field model associated to the Huang — Yang — Luttinger model of a boson gas with hard — sphere repulsion, using the so-called method of infrared bounds1-8. For this system we proved the existence of Bose — condensation

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