Nonextensive Statistical Mechanics

5.7 A Conjecture on the Time and Size Dependences of Entropy 199Fig. 5.50 The exponent κ as a function of α/d for the d = 1, 2, 3 α- XY model. The points for thed = 1 case are those of the inset of Fig. 5.47. The solid line is a guide to the eye consistent withuniversality. For α = 0wehaveκ(0) = 1/3 [179] (from [178]).Fig. 5.51 ˜λ maxN(N) forthe(α, d) = (0.8, 2) model for two different values of energy density u.The asymptotic N behavior, for all values of u > u c and 0 ≤ α/d < 1, appears to be ˜λ maxN(N) ∼A/N κ(α/d) ,whereA decreases from a finite, (α, d)-dependent, value to zero when u increases fromu c to infinity (from [178]).Fig. 5.52 α/d-dependance of 3 × κ metastable (full circles). Open triangles, circles, and squaresrespectively correspond to κ d of the d = 1, 2, 3 models [177, 178]. The arrow points to 1/3, valueanalytically expected [179–181] to be exact for α = 0andu > u c (from [376]).