# Non-Universal Equation of State of the Two-Dimensional Bose Gas

## TL;DR

This paper derives non-universal corrections to the equation of state of a two-dimensional Bose gas by accounting for finite-range effects, revealing complex dependencies on system parameters beyond the universal logarithmic form.

## Contribution

It presents a novel analytical approach to include finite-range effects in the equation of state of 2D Bose gases, extending beyond mean-field approximations.

## Key findings

- Pressure depends nonpolynomially on the finite-range parameter.
- Quantum fluctuations lead to complex, nontrivial dependencies on chemical potential and temperature.
- Results are obtained using dimensional regularization within a finite-temperature functional integral framework.

## Abstract

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 non-universal corrections to this equation of state taking account finite-range effects of the inter-atomic 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.