Simulation of 2D dynamical triangulation with higher order curvature terms

Phase Structure of Four-Dimensional Simplicial Quantum Gravity with a U(1) Gauge Field

“…3) we obtain ∆ = 0.4(1), Γ ∼ 0.5 (3). These values are apparently smaller than 1, the value they have in the pure gravity case.…”

“…We see that the shape of the distribution function is very similar to that in the two-dimensional case. 4), 3) The similarity to the two-dimensional case is most apparent. This indicates that a conformal mode in four-dimensions may be dominant as well.…”

“…In two-dimensions, gravity can be quantized when the central charge c is less than or equal to 1. The method of dynamical triangulation is regarded as a valid discretized model and has given results consistent with analytical approaches, for example, the MINBU analysis, 1), 2) the loop length distributions, 3), 4) and the string susceptibility. 5) Recently, numerical studies in four-dimensions using the method of dynamical triangulation in analogy to the two-dimensional model have been carried out.…”

“…From the investigation of two-dimensional simplicial gravity, 3) it was indicated that the scaling structure of the boundaries provides more information than the Hausdorff dimension. We note that in twodimensional simplicial gravity, the boundary length (the loop length L) distribution function has been found analytically 4) as a function of the scaling variable x = L/D 2 :…”

“…We determined the volume of the mother boundary as a function of D. In Fig. 9 we plot the mother boundary volume V (3) with the size of N 4 = 32K at the critical point. This figure exhibits the scaling, and we find that the scaling parameter is α = 3.7 (5).…”