Abstract

The truncated pair function for a particular system of random surfaces on Z d is analyzed for all temperatures strictly below the critical temperature. Throughout this regime, it is shown that (i) the pair function has Ornstein-Zernike behavior, (ii) the mass, or inverse correlation length, is analytic, (iii) the number of random surfaces has the expected asymptotic scaling, and (iv) the surfaces do not undergo a breathing transition. The results are established by using a random-surface Schwinger-Dyson equation which should be applicable in the nonperturbative analysis of other models of random paths and surfaces.

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