Monte Carlo Simulations with Indefinite and Complex-Valued Measures

TL;DR

This paper introduces a new Monte Carlo simulation method that effectively addresses the sign problem in systems with indefinite or complex measures, demonstrating improved accuracy and feasibility over traditional approaches.

Contribution

The paper presents a novel Monte Carlo approach for systems with complex or indefinite measures, outperforming crude methods and enabling simulations where previous techniques failed.

Findings

Significantly reduced statistical errors compared to crude Monte Carlo.

Successful application to exactly solvable Ising models with complex parameters.

Demonstrated workability even when traditional methods fail.

Abstract

A method is presented to tackle the sign problem in the simulations of systems having indefinite or complex-valued measures. In general, this new approach is shown to yield statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. Exactly solvable, one-dimensional Ising models with complex temperature and complex activity illustrate the considerable improvements and the workability of the new method even when the crude one fails.