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Phase structure of the O(n) model on a random lattice for n > 2

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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 γ = +1/2 or there exists a dual critical point with negative string susceptibility exponent, γ̃, related to γ by γ = γ̃/γ̃-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 (γ̃, γ) = (-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.

OriginalsprogEngelsk
TidsskriftNuclear Physics B
Vol/bind483
Udgave nummer3
Sider (fra-til)535-551
Antal sider17
ISSN0550-3213
DOI
StatusUdgivet - 13 jan. 1997

ID: 186919615