Using renormalization group (RG) analyses and Monte Carlo (MC) simulations, we study the fully packed dimer model on the bilayer square lattice with fugacity equal to $z$ (1) for interlayer (intralayer) dimers, and intralayer interaction $V$ between neighboring parallel dimers on any elementary plaquette in either layer. For a range of not-too-large $z>0$ and repulsive interactions $0<V<V_s$ (with $V_s\approx 2.1$), we demonstrate the existence of a bilayer Coulomb phase with purely dipolar two-point functions, i.e., without the power-law columnar order that characterizes the usual Coulomb phase of square and honeycomb lattice dimer models. The transition line $z_c\left(V\right)$ separating this bilayer Coulomb phase from a large-$z$ disordered phase is argued to be in the inverted Kosterlitz-Thouless universality class. Additionally, we argue for the possibility of a tricritical point at which the bilayer Coulomb phase, the large-$z$ disordered phase and the large-$V$ staggered phase meet in the large-$z$, large-$V$ part of the phase diagram. In contrast, for the attractive case with $V_{cb}<V\le 0$ $(V_{cb}\approx -1.2)$, we argue that any $z>0$ destroys the power-law correlations of the $z=0$ decoupled layers, and leads immediately to a short-range correlated state, albeit with a slow crossover for small $\left|V\right|$. For $V_c<V<V_{cb}$ $(V_c\approx -1.55)$, we predict that any small nonzero $z$ immediately gives rise to long-range bilayer columnar order although the $z=0$ decoupled layers remain power-law correlated in this regime; this implies a nonmonotonic $z$ dependence of the columnar order parameter for fixed $V$ in this regime. Further, our RG arguments predict that this bilayer columnar ordered state is separated from the large-$z$ disordered state by a line of Ashkin-Teller transitions $z_{\mathrm{AT}}\left(V\right)$. Finally, for $V<V_c$, the $z=0$ decoupled layers are already characterized by long-range columnar order, and a small nonzero $z$ leads immediately to a locking of the order parameters of the two layers, giving rise to the same bilayer columnar ordered state for small nonzero $z$.

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二维二聚体模型的双层库仑相：幂律柱状阶的缺失

使用重归一化组（RG）分析和蒙特卡洛（MC）模拟，我们研究了逸度等于 $ž$ （1）用于层间（层内）二聚体和层内相互作用 $\mathrm{伏特}$在任一层中任何基本块状体上相邻的平行二聚体之间。对于范围不太大的范围$ž>0$ 和排斥相互作用 $0<\mathrm{伏特}<{\mathrm{伏特}}_s$ （和 ${\mathrm{伏特}}_s\approx 2.1$），我们证明了具有纯偶极两点函数的双层库仑相的存在，即没有幂律柱状阶来表征正方形和蜂窝晶格二聚体模型的通常库仑相。过渡线${ž}_C（\mathrm{伏特}）$ 将该双层库仑相与大的$ž$据认为，无序阶段属于倒置的Kosterlitz-Thouless普遍性类别。此外，我们提出了三重临界点的可能性，在该临界点上，双层库仑相$ž$ 无序相和大$\mathrm{伏特}$ 交错相遇在大$ž$， 大-$\mathrm{伏特}$相图的一部分。相反，对于具有吸引力的情况${\mathrm{伏特}}_{Cb}<\mathrm{伏特}\le 0$ $（{\mathrm{伏特}}_{Cb}\approx -1.2）$，我们认为 $ž>0$ 破坏了幂律相关性 $ž=0$ 解耦的层，并立即导致短距离相关状态，尽管对于较小的交叉速度很慢 $\left|\mathrm{伏特}\right|$。为了${\mathrm{伏特}}_C<\mathrm{伏特}<{\mathrm{伏特}}_{Cb}$ $（{\mathrm{伏特}}_C\approx -1.55）$，我们预测任何小的非零值 $ž$立即产生远距离双层柱状顺序，尽管$ž=0$在这种情况下，解耦层仍保持幂律相关性；这意味着非单调$ž$ 固定的列序参数的依赖性 $\mathrm{伏特}$在这种制度下。此外，我们的RG论证预测，这种双层柱状有序状态与大的$ž$ 一系列Ashkin-Teller转换引起的无序状态 ${ž}_{在}（\mathrm{伏特}）$。最后，对于$\mathrm{伏特}<{\mathrm{伏特}}_C$， 这 $ž=0$ 解耦的层已经以远距离的柱状顺序和一个小的非零为特征 $ž$ 立即导致两层顺序参数的锁定，从而对于较小的非零值产生相同的双层柱状有序状态 $ž$。