标题： 三维空间中具有立方扰动的$O(2)$不变$φ^4$理论的蒙特卡罗研究 显示英文标题

标题： Monte Carlo study of the $O(2)$-invariant $φ^4$ theory with a cubic perturbation in three dimensions

摘要： 我们研究在存在立方对称性或等效的$\mathbb{D}_4$对称性扰动的情况下，在简单立方晶格上的$2$组分$\phi^4$模型。 为此，我们结合蒙特卡罗模拟和数据的有限尺寸标度分析。 我们遵循之前对$3$组分情况的研究。 我们研究从解耦的伊辛固定点到$O(2)$对称性固定点的RG流，以及向由涨落诱导的一阶相变方向的流动。 为此，我们研究了现象学耦合的行为。 在$O(2)$对称性固定点，我们得到了扰动的RG指数$Y_4=-0.1118(10)$的估计值。 注意，$Y_4$的小模量意味着 RG 流是缓慢的。 因此，为了解释实验或格点模型的蒙特卡洛模拟，这些模型由带有立方项的$\phi^4$模型有效描述，我们必须考虑固定点邻域之外的 RG 流。 显示英文摘要

摘要： We study the $2$-component $\phi^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size scaling analysis of the data. We follow previous work on the $3$-component case. We study the RG flow from the decoupled Ising fixed point into the $O(2)$-invariant one and towards the fluctuation induced first order transition. To this end we study the behavior of phenomenological couplings. At the $O(2)$-invariant fixed point we obtain the estimate $Y_4=-0.1118(10)$ of the RG-exponent of the perturbation. Note that the small modulus of $Y_4$ means that the RG flow is slow. Hence, in order to interpret experiments or Monte Carlo simulations of lattice models, which are effectively described by the $\phi^4$ model with a cubic term, we have to consider the RG flow beyond the neighborhood of the fixed points.