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Geometrical string and dual spin systems
Institution:1. Physics Department, Faculty of Science, Damietta University, Damietta 34517, Egypt;2. Chemistry Department, Faculty of Science, Damietta University, Damietta 34517, Egypt;1. Chemistry Department, Faculty of Science, Damietta University, Damietta, Egypt;2. Environmental Monitoring Laboratory, Ministry of Health, Port Said, Egypt
Abstract: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 ∧μ, η = ∧η,μ N. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). 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 F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.
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