Amoeba Monte Carlo algorithms for random trees with controlled branching activity: efficient trial move generation and universal dynamics

TL;DR

This paper introduces generalized Amoeba Monte Carlo algorithms for efficiently simulating random trees with controlled branching activity, revealing a new scaling regime in their relaxation dynamics.

Contribution

It extends the Amoeba algorithm to handle random trees with controlled branching, analyzing their relaxation dynamics and uncovering a novel scaling behavior.

Findings

Amoeba algorithms effectively equilibrate random trees with controlled branching.

Discovered a new scaling regime with relaxation time scaling as N^2 times the mean segment count to the power 0.4.

Relaxation dynamics exhibit rich behavior with implications for polymer and tree simulations.

Abstract

The reptation Monte Carlo algorithm is a simple, physically motivated and efficient method for equilibrating semi-dilute solutions of linear polymers. Here we propose two simple generalizations for the analogue {\it Amoeba} algorithm for randomly branching chains, which allow to efficiently deal with random trees with controlled branching activity. We analyse the rich relaxation dynamics of Amoeba algorithms and demonstrate the existence of an unexpected scaling regime for the tree relaxation. In particular, our results suggests that the equilibration time for Amoeba algorithms scales in general like $N^2 \langle n_{\rm lin}\rangle^\Delta$, where $N$ denotes the number of tree nodes, $\langle n_{\rm lin}\rangle$ the mean number of linear segments the trees are composed of and $\Delta \simeq 0.4$.