Finite-temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture

We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures dilute ultracold atomic gases. use a mean-field Hartree-Fock theory to derive analytical predictions for miscible-immiscible transition. A nontrivial result this is that fully miscible phase at $T=0$ may become unstable $T\neq0$, as consequence divergent behaviour spin susceptibility. test prediction by performing numerical simulations with Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond effects. calculate equilibrium configurations different temperatures and interaction strengths we simulate oscillations produced weak external perturbation. Despite some qualitative agreement, comparison between two theories shows approximation not able properly describe behavior mixture near transition, smoothen all sharp features both diagram dynamics, except temperature well below critical superfluidity.