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.
|Number of pages||12|
|Journal||Nuclear Physics B|
|Publication status||Published - 8 Mar 1999|