论文标题
二维二聚体模型的双层库仑相：不存在幂律柱状订单
Bilayer Coulomb phase of two dimensional dimer models: Absence of power-law columnar order
论文作者
论文摘要
我们研究了双层平方晶格上的完全包装的二聚体模型，其散发性等于$ z $（$ 1 $）的层间二聚体（内部内部）二聚体，以及在任何一层的任何基本plaquette上相邻的平行二聚体之间的内部交互$ v $。对于一系列不太大的$ z> 0 $和排斥互动$ 0 <v <v_s $（带有$ v_s \约2.1 $），我们证明存在一个{\ em biyer coulomb phoes}，并具有纯粹的二极性二极化的两点两点函数，而没有蜂蜜级的均值和蜂蜜级的均值，并逐渐缩写蜂蜜的阶段。型号。过渡线$ z_ {c}（v）$将这个双层库仑阶段与大$ z $ avery阶段分开，被认为是倒置的kosterlitz-无尽的普遍性类。此外，我们争辩说，双层库仑阶段，大$ z $无序阶段和大$ v $交错的相遇的可能性是，大$ z $，大$ z $，大$ v $部分相位图。相反，对于具有$ v_ {cb} <v \ leq 0 $（$ v_ {cb} \约-1.2 $）的有吸引力的情况，我们争辩说，任何$ z> 0 $ destrouns powerlaw的相关性损坏了$ z = 0 $ decoupled层的幂律相关性，并立即与短范围的状态相处，以$ corled cormeld cormerled contrand control a n y $ $ $ $ $ c。对于$ v_ {c} <v <v_ {cb} $（$ v_ {c} \大约-1.55 $），我们预测，任何一个小的非零$ z $立即引起了远距离{\ em biyer columnar订单}，尽管$ z = 0 $ decpled layers在此制度中保持了电源相关性。这意味着该制度中固定$ v $的列订单参数的非单调$ z $依赖性。该双层柱订购状态与Ashkin-Teller Transitions $ z _ {\ rm at}（v）$的一行与大的$ z $ chaper状态分开。
We study the fully-packed dimer model on the bilayer square lattice with fugacity equal to $z$ ($1$) for inter-layer (intra-layer) dimers, and intra-layer interaction $V$ between neighbouring 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 {\em bilayer Coulomb phase} with purely dipolar two-point functions, {\em i.e.}, without the power-law columnar order that characterizes the usual Coulomb phase of square and honeycomb lattice dimer models. The transition line $z_{c}(V)$ 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 \leq 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 $|V|$. For $V_{c} < V < V_{cb}$ ($V_{c} \approx -1.55$), we predict that any small nonzero $z$ immediately gives rise to long-range {\em bilayer columnar order} although the $z=0$ decoupled layers remain power-law correlated in this regime; this implies a non-monotonic $z$ dependence of the columnar order parameter for fixed $V$ in this regime. This bilayer columnar ordered state is separated from the large-$z$ disordered state by a line of Ashkin-Teller transitions $z_{\rm AT}(V)$.
