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From Z(T, V ), all thermodynamical observables can be calculated in the usual fashion. Thus = T2 V ∂ ln Z ∂T (12) V gives the energy density, and P =T ∂ ln Z ∂V (13) T the pressure. For the study of critical behavior, long range correlations and multi-particle interactions are of crucial importance; hence perturbation theory cannot be used. The necessary non-perturbative regularisation scheme is provided by the lattice formulation of QCD [14]; it leads to a form which can be evaluated numerically by computer simulation [15].

Given N disks, the disk density is n = N/A. Clearly, the average cluster S(n) size will increase with n. The striking feature is that it does so in a very sudden way (see Fig. 12); as n approaches some “critical value” nc , S(n) suddenly becomes large enough to span the surface A. In fact, in the limit N → ∞ and A → ∞ at constant n, both S(n) and dS(n)/dn diverge for n → nc : we have percolation as a geometric form of critical behavior. , when we have of different systems. In two dimensions, disks percolate at np a little more than one disk per unit area.

Rev. D 67 (2003) 114504. V. Goloviznin and H. Satz, Z. Phys. C 57 (1993) 671. F. Karsch, A. Patkos and P. Petreczky, Phys. Lett. B 401 (1997) 69. K. Redlich and H. Satz, Phys. Rev. D 33 (1986) 3747. 1 The States of Strongly Interacting Matter [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] 25 M. , Phys. Rev. D 58 (1998) 096007; M. Stephanov, K. Rajagopal and E. Shuryak, Phys. Rev. Lett. 81 (19989) 4816. Z. Fodor and S. Katz, JHEP 0203 (2002) 014.

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