Figure 1: K C 4 versus Ln(n 4 ) for K 2 = 0. Values for N
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چکیده
16 The second possibility (which is the most interesting one) is that the measure factor changes the universality class. Our results, albeit preliminary, seem to hint in this direction. In this case we could have a critical value of n c , and transitions belonging to diierent universality classes. This is a very appealing scenario, and here the lattice theory could make its own original contribution. It could be possible to pick out the correct measure, on the lattice, by requiring a particular expectation value and scaling behavior of some physical observable. Such a prescription would be a powerful tool, turning the discrete version of the theory from a source of indetermination into a completely determined scheme. 5 Conclusions It is not easy to summarize such an evolving scenario. Things look good, and interesting. The number of triangulation does not seem to increase in a pathological way, and the exponential bound seems to be valid. This is the rst evidence that makes our hope of nding interesting phenomena stronger. Diierent models based on diierent choices of the lattice measure have quite diierent behaviors. One will have to investigate in more detail if all the lattice theories will have the same continuum behavior or if we are nding a more complex phase diagram. Finally, the new results of 12] seem to fortify the hope that a critical theory could be generated at one point of the phase diagram. Simplicial quantum gravity looks like a promising eld, deenitely worth of further investigations. Both gures show that the measure operator has a pronounced eeect. Increasing the coupling of the measure term leads to a continuous, monotonous deformation of the curves. Notice that the curves are not just shifted. In the case of R=V , the singularity seems stronger for n ' 0, where the jump in R=V is quite sharp. The distance d has a sharper jump for n = 1, where it seems to jump from one constant value to another constant. Smaller values of n show a slower increase in d. For large absolute values of n, especially for n = ?5, the plots show a weaker singular-ity. The proole of R=V hints less at a sharp jump than the former cases, and the distance increases very smoothly from a critical value of k 2 , k c 2 (n), on. When n increases to the value of 5 the system …
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