Exact solution of the three-dimensional (3D) Z2 lattice gauge theory

Abstract

In this work, the origin of nonlocal effects is inspected and the contributions of nontrivial topological structures to physical properties are investigated in details for both the 3D Ising model and the Z2 lattice gauge model. Then the exact solution for the 3D Z2 lattice gauge theory is derived by the duality between the two models. Several fundamental issues, such as dimensionality, duality, symmetry, manifold, degenerate states, are investigated for these many-body interacting spin systems. The connections with superfluid, superconductors, etc. are evaluated. Furthermore, physical significances and mathematical aspects of the 3D Z2 lattice gauge theory are discussed with respect to topology, geometry, and algebra.

arXiv comment52 pages, 5 figures, corrections are made on Eq. (9)

References in corpus (18)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Critical Phenomena and Renormalization-Group Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Historical roots of gauge invariance
• Conjectures on exact solution of three - dimensional (3D) simple orthorhombic Ising lattices
• Critical behavior of the van der Waals bonded ferromagnet Fe${}_{3-x}$GeTe${}_2$
• Clifford algebra approach of 3D Ising model
• Computational complexity of spin-glass three-dimensional (3D) Ising model
• Quaternions and Special Relativity
• Series studies of the Potts model. I: The simple cubic Ising model
• Mathematical structure of three - dimensional (3D) Ising model
• Exact solution of two-dimensional (2D) Ising model with a transverse field: a low-dimensional quantum spin system
• A Brief Introduction to Wilson Loops and Large N
• Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem
• Response to arXiv:0811.3876 "Comment on a recent conjectured solution of the three dimensional Ising model" by Wu et al
• Response to arXiv:0811.1802 "Comment on 'Conjectures on exact solution of three-dimensional (3D) Ising lattices'" by Perk and Singularities at/near infinite temperature: Reply to Perk's Rejoinder arXiv:0901.2935
• Topological Quantum Statistical Mechanics and Topological Quantum Field Theories
• Lower bound of computational complexity of knapsack problems

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• Exact solution of a two-dimensional (2D) Ising model with the next nearest interactions
• Equivalence between the zero distributions of the Riemann zeta function and a two-dimensional Ising model with randomly distributed competing interactions