Abstract
We supply numerical evidence for the existence of critical dimensions d c 1 and d c 2 gaussian model of a discretized string, between which the mean number of vertices in the world sheet diverges, and hence a continuum limit may exist. We also discuss the possibility of non-trivial continuum limits. In particular, by introducing an additional parameter into the model, we argue that non-trivial continuum limits can possibly be obtained only between two critical dimensions d′ 0 and d 0. Furthermore, we give proofs of some lower bounds on determinants of combinatorial laplacians entering the models, which were announced in a previous paper.
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