An improved algorithm for dynamical triangulations and simulations of finer lattices

Abstract

We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of local and global terms in the action, a condition needed for efficient simulation of theories with global terms, while still maintaining detailed balance. We test our algorithm on the $2d$ Ising model, and against results for EDT obtained with standard Metropolis. Our new algorithm allows us to simulate EDT at finer lattice spacings than previously possible, and we find geometries that resemble semiclassical Euclidean de Sitter space in agreement with earlier results at coarser lattices. The agreement between lattice data and the classical de Sitter solution continues to get better as the lattice spacing decreases.