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A note on the three-dimensional Ising model as a string theory

Jacques Distler

1992
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Nuclear Physics B
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It has long been argued that the continuum limit of the 3D Ising model is equivalent to a string theory. Unfortunately, in the usual starting point for this equivalence -- a certain lattice theory of surfaces -- it is not at all obvious how to take the continuum limit. In this note, I reformulate the lattice theory of surfaces in a fashion such that the continuum limit is straightforward. I go on to discuss how this new formulation may overcome some fundamental objections to the notion that the
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... Ising model is equivalent to a string theory. In an appendix, I also discuss some aspects of fermion doubling, and the lattice fermion formulation of the 2D Ising model.

doi:10.1016/0550-3213(92)90558-s
fatcat:uqn445gvyng5bio4yn5lq2mz54