Canonical simulations with worldlines: an exploratory study in $\phi^{4}_{2}$ lattice field theory

TL;DR

This paper explores canonical simulation methods using worldline formulations in 2D lattice $\,\phi^4$ theory, detailing algorithms and data conversion techniques for broader application.

Contribution

It introduces a canonical worldline simulation approach for lattice field theories, providing detailed algorithms and demonstrating its potential for generalization.

Findings

Developed a canonical worldline simulation framework.

Outlined data conversion from canonical to grand canonical ensembles.

Validated the approach with cross-checks against grand canonical results.

Abstract

In this letter we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged $\phi^4$ field in two dimensions as an example we present the details of the canonical formulation based on worldlines and outline algorithmic strategies for canonical worldline simulations. We discuss the steps for converting the data from the canonical approach to the grand canonical picture which we use for cross-checking our results. The canonical approach presented here can easily be generalized to other lattice field theories with a worldline representation.