Phase diagram of the mean field model of simplicial gravity

P. Bialas, Z. Burda, D. Johnston

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


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 p(q) = q¯ß, which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases: elongated (fluid) and crumpled. For ß ? (2, 8) the transition between these two phases is first-order, while for ß ? (1, 2] it is continuous. The transition becomes softer when ß approaches unity and eventually disappears at ß = 1. 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 condensed phase appears in the phase diagram. It bears some similarity to the crinkled phase of simplicial gravity discussed recently in models of gravity interacting with matter fields. © 1999 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)413-424
Number of pages12
JournalNuclear Physics B
Issue number1-2
Publication statusPublished - 8 Mar 1999


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