# Large-$N$ expansion for condensation and stability of Bose-Bose mixtures at finite temperatures

## TL;DR

This paper uses large-N expansion to analyze the stability and condensate density of two-component Bose mixtures at finite temperatures, highlighting the role of thermal excitations in phase diagram formation.

## Contribution

It introduces a large-N expansion approach to study finite-temperature effects on Bose-Bose mixtures, providing new insights into their stability and phase behavior.

## Key findings

- Finite-temperature excitations significantly influence phase stability.
- The condensate density depends on temperature and interaction parameters.
- The phase diagram of Bose mixtures is shaped by thermal effects.

## Abstract

The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state below the Bose-Einstein transition point and the temperature dependence of the condensate density for symmetric mixture of Bose gases. The presented analysis reveals the importance of finite-temperature excitations of the non-condensed particles in formation of the phase diagram of two-component Bose systems.