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Phase Structure of the O(n) Model on a Random Lattice for n>2

B. Durhuus·C. Kristjansen
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Abstract

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either \g=+1/2 or there exists a dual critical point with negative string susceptibility exponent, \g', related to \g by \g=\g'/(\g'-1). Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n>2 and that the possible dual pairs of string susceptibility exponents are given by (\g',\g)=(-1/m,1/(m+1)), m=2,3,.... We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite.

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B. Durhuus, C. Kristjansen. 1996-08-30. Phase Structure of the O(n) Model on a Random Lattice for n>2. https://doi.org/10.1016/s0550-3213(96)00574-3

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