Phase diagram of the mean field model of simplicial gravity
arXiv:gr-qc/9808011 · doi:10.1016/S0550-3213(98)00842-6
Abstract
We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form , which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases~: {\em elongated} ({\em fluid}) and {\em crumpled}. For the transition between these two phases is first order, while for it is continuous. The transition becomes softer when approaches unity and eventually disappears at . We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new {\em condensed} phase appears in the phase diagram. It bears some similarity to the {\em crinkled} phase of simplicial gravity discussed recently in models of gravity interacting with matter fields.
15 pages, 5 figures
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