### 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 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 language | English |
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Pages (from-to) | 413-424 |

Number of pages | 12 |

Journal | Nuclear Physics B |

Volume | 542 |

Issue number | 1-2 |

Publication status | Published - 8 Mar 1999 |

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## Cite this

*Nuclear Physics B*,

*542*(1-2), 413-424.