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arXiv · hep-th/9308094

Geometrical String and Spin Systems

G. K. Savvidy·F. J. Wegner
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Abstract

We formulate a new geometrical string on the euclidean lattice. It is possible to find such spin systems with local interaction which reproduce the same surface dynamics.In the three-dimensional case this spin system is a usual Ising ferromagnet with additional diagonal antiferromagnetic interaction and with specially adjusted coupling constants. In the four-dimensional case the spin system coincides with the gauge Ising system with an additional double-plaquette interaction and also with specially tuned coupling constants. We extend this construction to random walks and random hypersurfaces (membrane and p-branes) of high dimensionality. We compare these spin systems with the eight-vertex model and BNNNI models.

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G. K. Savvidy, F. J. Wegner. 1993-08-19. Geometrical String and Spin Systems. https://doi.org/10.1016/0550-3213(94)90003-5

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