Effective Sampling of Random Surfaces by Baby Universe Surgery

TL;DR

This paper introduces a highly efficient algorithm for sampling random surfaces in Monte Carlo simulations, significantly reducing autocorrelation times and enabling larger simulations involving matter fields.

Contribution

The paper presents a novel baby universe surgery algorithm that outperforms standard local flip methods in sampling efficiency for random surfaces.

Findings

Reduces autocorrelation time by three orders of magnitude.

Enables simulation of large random surfaces with matter fields.

Demonstrates effectiveness on 2D simplicial gravity with scalar fields.

Abstract

We propose a new, very efficient algorithm for sampling of random surfaces in the Monte Carlo simulations, based on so-called baby universe surgery, i.e. cutting and pasting of baby universes. It drastically reduces slowing down as compared to the standard local flip algorithm, thereby allowing simulations of large random surfaces coupled to matter fields. As an example we investigate the efficiency of the algorithm for 2d simplicial gravity interacting with a one-component free scalar field. The radius of gyration is the slowest mode in the standard local flip/shift algorithm. The use of baby universe surgery decreases the autocorrelation time by three order of magnitude for a random surface of $0.5 \cdot 10^5$ triangles, where it is found to be $\tau_{int} = 150 \pm 31$ sweeps.