Abstract
Abstract We introduce a generalized model of planar random surfaces (PRS) with a curvature term in the action. We establish the basic thermodynamic properties of the model, prove reflection positivity of the two-loop function and verify tree bounds, which imply that the critical exponent of the susceptibility is smaller than or equal to 1 2 . Critical properties of the model are discussed as well as the critical behaviour of the self-avoiding random surface model. The latter is shown not to have a breathing transition if the string tension is positive. Moreover, it is argued that its upper critical dimension is eight.
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