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

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二维Bose-Bose原子混合物的有限温度自旋动力学

我们研究了热波动在稀释的超冷原子气体的均匀二维二元Bose混合物中的作用。我们使用均场Hartree-Fock理论来得出可混溶-不可混溶转变的分析预测。这一理论的重要成果是，在$Ť=0$ 可能会变得不稳定 $Ť\ne 0$，这是自旋磁化率行为不同的结果。我们通过使用随机（预测的）Gross-Pitaevskii方程进行数值模拟来测试此预测，其中包括超出平均场的影响。我们计算了在不同温度和相互作用强度下的平衡构型，并模拟了由弱外部扰动产生的自旋振荡。尽管有一些定性的共识，但两种理论之间的比较表明，均值场近似无法正确描述二维混合物在混溶-非混溶转变附近的行为，因为热波动会平滑相中所有的尖锐特征图和自旋动力学，除了温度远低于超流的临界温度。