3.6 Evidence for a second-order transition?

The same ldl-measure was used by Hamber in an extension of a previous simulation of the higher-derivative action (16View Equation[113Jump To The Next Citation Point], for lattice sizes of up to 164. At the transition point (k = kc ≃ 0.244, λ = 1, a = 0.005), the distributions of edge lengths, volumes and curvatures are smooth and Gaussian-like, and the average curvature vanishes. The location of k (a) c from fits (17View Equation) to the average curvature coincide with those from [111Jump To The Next Citation Point], leading to δ ≃ 0.626. The data at a = 0 do not seem to match this interpretation. This leads to the tentative conclusion that only for sufficiently large a the observed transition is of second order. It is in general “difficult to entirely exclude the presence of a weak first-order transition, if it has a very small latent heat”. For a = 0.005, one finds some evidence for a decrease in the fractal dimension as k grows.
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