Abstract
By making an exact mapping of the resonant-valence-bond state to a classical O(4) model in a logarithmic potential, Shapir and Kohmoto recently obtained a mean-field estimate for the norm of the wave function from the partition function of the classical model. Their mean-field estimate is expected to be correct in high dimensions (only). We discuss the partition function of the loop-gas model, Z(x,y), on the honeycomb lattice for various values of the fugacities x and y and obtain as a special case an approximation for Z(2,4), the norm of the wave function, which should be quite reasonable for the two-dimensional case considered here.
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