Nonuniversal Equation of State of the Two-Dimensional Bose Gas

For a dilute two-dimensional Bose gas the universal equation of state has a logarithmic dependence on the $s$-wave scattering length. Here we derive nonuniversal corrections to this equation of state, taking account of finite-range effects of the interatomic potential. Our beyond-mean-field analytical results are obtained performing dimensional regularization of divergent zero-point quantum fluctuations within the finite-temperature formalism of functional integration. In particular, we find that in the grand canonical ensemble the pressure has a nonpolynomial dependence on the finite- range parameter and it is a highly nontrivial function of chemical potential and temperature.