Thermodynamics of the d   =  3  +  1 quantum XY model

Within effective field theory we explore the properties of the d   =  3  +  1 quantum XY model at low temperatures and in weak magnetic or staggered fields. For this parameter regime only few results appear to be known, and furthermore are restricted to one-loop order. In the present study we systematically analyze the thermodynamics of the d   =  3  +  1 quantum XY model up to three-loop order. In the low-temperature expansion of the free energy density, the free Bose gas term of order T  ⁴ receives corrections of order T  ⁶ and T  ⁸. The discussion also includes the pressure, (staggered) magnetization and susceptibility. In particular, we show how these quantities are influenced by the spin-wave interaction. (paper: quantum statistical physics, condensed matter, integrable systems)