Scanning the critical fluctuations -- application to the phenomenology of the two-dimensional XY-model --

TL;DR

This paper introduces a magnetic-field scanning method to precisely analyze the probability distribution of the order parameter in the 2D XY-model, challenging previous conjectures about its asymptotic behavior.

Contribution

It demonstrates how field conjugated to the order parameter can serve as a precise probe, providing new insights into the critical fluctuations of the 2D XY-model.

Findings

Disproved the double-exponential conjecture for large-magnetization asymptote.

Established magnetic-field scanning as an effective tool for studying critical fluctuations.

Provided detailed numerical analysis of the 2D XY-model's order parameter distribution.

Abstract

We show how applying field conjugated to the order parameter, may act as a very precise probe to explore the probability distribution function of the order parameter. Using this `magnetic-field scanning' on large-scale numerical simulations of the critical 2D XY-model, we are able to discard the conjectured double-exponential form of the large-magnetization asymptote.