String tension in a lattice model of random surfaces

Abstract

The model of planar random surfaces without spikes shows nontrivial critical behaviour on a four-dimensional lattice. In this article we address ourselves to the question of whether the string tension has a finite continuum limit at the critical point. To this end we calculated the first few terms of its strong coupling expansion and analysed them with the help of Padé approximants. The results indicate a nonvanishing critical string tension in lattice units which implies that the physical string tension would diverge in the continuum limit. We applied the method to the susceptibility too and found values for its critical exponent which are consistent with the Monte Carlo results, supporting the reliability of the method.