Beyond the c=1 barrier in two-dimensional quantum gravity

Thorleifsson G, Petersson B. Beyond the c=1 barrier in two-dimensional quantum gravity. In: Nuclear Physics B - Proceedings Supplements. NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS. Vol 63. ELSEVIER SCIENCE BV; 1998: 745-747.We introduce a simple model of touchingrandom surfaces, by adding a chemical potential rho for "minimal necks", and study this model numerically coupled to a Gaussian model in d-dimensions (for central charge c = d = 0, 1 and 2). For c less than or equal to 1, this model has a phase transition to branched polymers, for sufficiently large p. For c 2, however, extensive simulations indicate that this transition is replaced by a cross-over behavior on finite lattices - the model is always in the branched polymer phase. This supports recent speculations that, in 2d-gravity, the behavior observe in simulations for c less than or equal to 1, is dominated by finite size effects, which are exponentially enhanced as c --> 1(+)