论文标题
（四）双plaquette 3D ising模型
(Four) Dual Plaquette 3D Ising Models
论文作者
论文摘要
3D Plaquette Ising模型的一个特征是其平面子系统对称性。该模型的量子版本已被证明是通过与X-Cube模型的二元性相关的，X-Cube模型在新的且快速发展的分布群领域一直是范式的。 3D Plaquette Ising和X-Cube模型之间的关系与2D量子横向旋转ising模型与圆环代码之间的关系。在2D ISING模型的情况下测量全局对称性，并考虑高温阶段的规格不变扇区导致折叠代码，而在测量3D量子横向旋转式Plaquette ISING模型的子系统对称模型会导致X-Cube模型。 3D Plaquette Ising模型的一种非标准双表配方，该模型最近在对X-Cube模型的无fracton扇区进行双重划分的背景下进行了讨论。在本文中，我们研究了这种非标准双重汉密尔顿的经典自旋版本，并讨论了其与更熟悉的类似Ashkin-Teller的双重双重和进一步相关的双重配方有关的特性，涉及Link和Vertex旋转和非旋转。
A characteristic feature of the 3d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3d plaquette Ising and the X-Cube model is similar to that between the 2d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin-Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.
