1995/03/30 by G. K. Savvidy, G.K. Savvidy, K. G. Savvidy +3 · 33 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Duality (order theory) #Gauge theory #Hamiltonian (control theory) #Ising model #Quantum many-body systems #Spin (aerodynamics) #Spins #String (physics) #hep-th
paper · pdf · doi:10.1016/0550-3213(95)00151-h
published in Nuclear Physics B 443(3), 565-580 (Elsevier BV) · 16 pages,Latex
arxiv created 1995/03/30 · openalex publication_date 1995/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge Hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual Hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d(d-1)/2 Ising spins Λμ,ν= Λν,μ, μ≠ ν= 1,..,d and one Ising spin Γ on every link (ξ,ξ+eμ). For the frozen spin Γ≡ 1 the dual Hamiltonian factorizes into d(d-1)/2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ≡ -1. For fluctuating Γ it is a sort of spin glass system with local gauge invariance. The generalization to p-branes is given.