Geometrical string and dual spin systems
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 twoplaquette 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, μN}. ≠ P = 1, … , d and one Ising spin Γ on every link ξξ + e,). For the frozen spin Γ 1 the dual hamiltonian factorizes into d ( d  1) /2 twodimensional Ising ferromagnets and into antiferromagnets in the case Γ 1. For fluctuating F it is a sort of spinglass system with local gauge invariance. The generalization to pmembranes is given.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)00151H
 arXiv:
 arXiv:hepth/9503213
 Bibcode:
 1995NuPhB.443..565S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 16 pages,Latex