Critical exponents and scaling invariance in the absence of a critical point

TL;DR

This paper challenges the traditional view of the paramagnetic-to-ferromagnetic transition as a second-order phase transition, showing that observed scaling behaviors can occur without a true critical point, due to complex domain structures.

Contribution

It demonstrates that scaling invariance can exist without a critical point, highlighting the role of domain structures and multiple length scales in phase transitions.

Findings

Power laws observed over many decades in ultrathin Fe films.

Singular behavior becomes analytic near the transition, indicating no true critical point.

Monte Carlo simulations reproduce experimental results including dipole interactions.

Abstract

The paramagnetic-to-ferromagnetic phase transition is believed to proceed through a critical point, at which power laws and scaling invariance, associated with the existence of one diverging characteristic length scale -- the so called correlation length -- appear. We indeed observe power laws and scaling behavior over extraordinarily many decades of the suitable scaling variables at the paramagnetic-to-ferromagnetic phase transition in ultrathin Fe films. However, we find that, when the putative critical point is approached, the singular behavior of thermodynamic quantities transforms into an analytic one: the critical point does not exist, it is replaced by a more complex phase involving domains of opposite magnetization, below as well as $above$ the putative critical temperature. All essential experimental results are reproduced by Monte-Carlo simulations in which, alongside the familiar exchange coupling, the competing dipole-dipole interaction is taken into account. Our results imply that a scaling behavior of macroscopic thermodynamic quantities is not necessarily a signature for an underlying second-order phase transition and that the paramagnetic-to-ferromagnetic phase transition proceeds, very likely, in the presence of at least two long spatial scales: the correlation length and the size of magnetic domains.