Improvement of efficiency in generating random $U(1)$ variables with Boltzmann distribution

TL;DR

This paper introduces an efficient rejection-based method for generating random $U(1)$ variables with Boltzmann distribution, optimized for parallel processing, with potential applications to other Monte Carlo distributions.

Contribution

It presents a novel rejection method with variable transformation that achieves high efficiency across all temperature ranges, suitable for parallel computing environments.

Findings

High efficiency across all temperature ranges

Effective for parallel and pipeline vector processing

Potential applicability to other Monte Carlo distributions

Abstract

A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling parameters, which makes the present method especially suitable for parallel and pipeline vector processing machines. Results of computer runs are presented to illustrate the efficiency. An idea to find such algorithms is also presented, which may be applicable to other distributions of interest in Monte Carlo simulations.