Finite-size scaling at infinite-order phase transitions

TL;DR

This paper introduces a new diverging observable for finite-size scaling analysis at infinite-order phase transitions, demonstrating its advantages over non-diverging observables through the example of the F-model.

Contribution

It proposes a novel observable that diverges at the critical point, improving finite-size scaling analysis for infinite-order phase transitions.

Findings

The new observable diverges at the critical point.

Non-diverging observables can lead to incorrect conclusions.

Diverging observables provide more reliable finite-size scaling analysis.

Abstract

For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of diverging at the critical point. Focussing on the example of the F-model we compare the analysis of this observable with that of another observable, which is also derived from the order parameter but does not diverge, as well as that of the associated susceptibility. We discuss the difficulties that arise in the finite-size scaling analysis of such systems. In particular we show that one may reach incorrect conclusions from large-system size extrapolations of observables that are not known to diverge at the critical point. Our work suggests that one should base finite-size scaling analyses for infinite-order phase transitions only on observables that are guaranteed to diverge.