Grand-canonical simulation of two-dimensional simplicial gravity

The string susceptibility exponents of dynamically triangulated 2-dimensional surfaces with various topologies, such as a sphere, torus and double-torus, were calculated by the grand-canonical Monte Carlo method. These simulations were made for surfaces coupled to $d$-Ising spins ($d$=0,1,2,3,5). In each simulation the area of surface was constrained to within 1000 to 3000 of triangles, while maintaining the detailed-balance condition. The numerical results show excellent agreement with theoretical predictions as long as $d \leq 2$.Comment: 9 pages, Latex include 5 postscript figures, using psfig.sty and cite.st

Scaling Behavior in 4D Simplicial Quantum Gravity

Scaling relations in four-dimensional simplicial quantum gravity are proposed using the concept of the geodesic distance. Based on the analogy of a loop length distribution in the two-dimensional case, the scaling relations of the boundary volume distribution in four dimensions are discussed in three regions: the strong-coupling phase, the critical point and the weak-coupling phase. In each phase a different scaling behavior is found.Comment: 12 pages, latex, 10 postscript figures, uses psfig.sty and cite.st

Minbu distribution of two dimensional quantum gravity: simulation result and semiclassical analysis

We analyse MINBU distribution of 2 dimensional quantum gravity. New data of R^2-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. The cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing force of R^2-term. The dependence on the central charge c_m\ and on the R^2-coupling are explained for the ordinary 2d quantum gravity and for R^2-gravity. The R^2-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles . The surface topology is that of a sphere

Common Structures in Simplicial Quantum Gravity

The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were measured numerically. For spherical boundary surfaces, we obtained a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes was investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in three- and four-dimensional simplicial quantum gravity.Comment: 10 pages, latex, 6 ps figures, uses cite.sty and psfig.st