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

N. Saratz, D. A. Zanin, U. Ramsperger, S. A. Cannas, D. Pescia, A. Vindigni

Published 2014-10-28Version 1

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 transition involving domains of opposite magnetization. Their size establishes a long spatial scale which persist alongside the correlation length, at any temperature, 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 interaction, the unavoidable, albeit weak, 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.