无缺陷的非均匀库仑模型是有病的：畴壁能按体积（而非边界面积）标度
Inhomogeneous Coulomb Models Without Defects are Sick: Domain Wall Energies Scaling as Volume (not Boundary Area)
AI总结：
本文证明，在无缺陷的情况下，满足散度为零约束的库仑模型存在病态行为，畴壁能随系统体积而非边界面积标度，并给出方格六顶点模型、量子二聚体和经典自旋冰中的例子。
摘要：
在这项工作中，我们展示了库仑模型——即满足 $\nabla\cdot\left\langle \mathbf{B}\right\rangle =0$ 无散约束的模型，其中 $\left\langle \mathbf{B}\right\rangle $ 是与晶格系统微观自由度相关的某些粗粒化变量——如果没有包含 $\nabla\cdot\mathbf{B}\neq0$ 的缺陷，则是有病的。我们证明，对于一般边界（其中边界上赝磁场的通量不抵消：$\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}\neq0$，这里 $\mathbf{n}$ 是单位法向，$\left\langle \mathbf{B}_{R/L}\right\rangle $ 是畴壁两侧的两个基态赝磁场），在没有缺陷的情况下，系统不同相之间的尖锐畴壁（宽度约为一个晶胞）的能量与系统大小（而非边界面积）成比例。我们在方格六顶点模型、量子二聚体以及存在磁场时的经典自旋冰中给出了这一现象的若干不同例子。我们还通过例子表明，条件 $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}=0$ 是边界兼容的必要但非充分条件——即畴壁能按畴壁面积而非系统大小标度。为了进一步说明边界条件在库仑系统中的重要性，我们证明系统边界，即使满足 $\int_{\partial V}\mathbf{B}\cdot\mathbf{n}=0$，也具有热力学后果——即亥姆霍兹自由能存在一个与系统大小广延的代价。
英文摘要：
In this work we show that coulomb models, ones that obey a $\nabla\cdot\left\langle \mathbf{B}\right\rangle =0$ divergence free constraint - for $\left\langle \mathbf{B}\right\rangle $ being some coarse grained variables related to the microscopic degrees of freedom of the lattice system - are sick without the inclusion of defects with $\nabla\cdot\mathbf{B}\neq0$. We show that for generic boundaries (ones where the fluxes of the pseudo-magnetic fields on the boundary do not cancel: $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}\neq0$ - here $\mathbf{n}$ is the unit normal and $\left\langle \mathbf{B}_{R/L}\right\rangle $ are the two ground state pseudo-magnetic fields on either side of the domain wall) without the inclusion of defects, sharp domain walls (on the order of the width of a unit cell) between different phases of the system cost energy proportional to system size (not boundary area). We present several different examples of this phenomena in the square lattice six vertex model, in quantum dimers and in classical spin ice in the presence of magnetic fields. We also show by example that the condition $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}=0$ is a necessary but not sufficient condition for the boundaries to be compatible - that is domain wall energy to scale with domain wall area and not system size. To further present the importance of boundary conditions in Coulomb systems we show that system boundaries, even ones that satisfy $\int_{\partial V}\mathbf{B}\cdot\mathbf{n}=0$, have thermodynamic consequences - that is there is a cost, extensive in system size, to the Helmholtz free energy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
