Note on the Metropolis Monte Carlo method on random lattices

Transfer matrix formalism for two-dimensional quantum gravity and fractal structures of space-time

“…In fact a numerical study for pure gravity shows a clear universal scaling behavior according to G(x). [8] As we can see in eq. ( 27), < L 0 > and < L 1 > include ǫ dependent non-universal part as a dominant contribution while < L n > for n ≥ 2 includes only universal part and thus is expected to show clear fractal behaviors.…”

Grand-Canonical Simulation of Two-Dimensional Simplicial Gravity

“…(12) on random lattices, see ref. [11]. For the case d = 0, when a dual loop is separated by two dual loops, two spins should be attached to the two dual loops, which counts four spin states; in the inverse case one of two neighboring spins should be taken out, which counts two spin states.…”

Two-dimensional dynamical triangulation using the grand-canonical ensemble

“…In these moves the ergodic property is automatically satisfied. However, we must treat the detailed valance carefully [8], since the total number of possible moves depends on N 0 and {q i }. The detailed valance equation, that the move should satisfy, between configurations A and B, is given by…”