Johnston Desmond A, Ranasinghe Ranasinghe P K C M
School of Mathematical and Computer Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK.
Department of Mathematics, University of Sri Jayewardenepura, Gangodawila, Nugegoda 10250, Sri Lanka.
Entropy (Basel). 2020 Jun 8;22(6):633. doi: 10.3390/e22060633.
A characteristic feature of the 3 d 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 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d 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.
三维面元伊辛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通过对偶性与X立方体模型相关，而X立方体模型在新的快速发展的分形子领域中具有典范性。三维面元伊辛模型与X立方体模型之间的关系类似于二维量子横向自旋伊辛模型与环面码之间的关系。在二维伊辛模型的情况下对对称性进行规范，并考虑高温相的规范不变扇区，会得到环面码，而对三维量子横向自旋面元伊辛模型的对称性进行规范会得到X立方体模型。最近在对X立方体模型的无分形子扇区进行对偶化的背景下，讨论了一种利用三种自旋味的三维面元伊辛模型的非标准对偶表述。在本文中，我们研究了这种非标准对偶哈密顿量的经典自旋版本，并讨论了它与更熟悉的类阿什金 - 泰勒对偶以及涉及键自旋和顶点自旋以及非伊辛自旋的进一步相关对偶表述相关的性质。
