AUTHOR=Contoyiannis Yiannis , Potirakis Stelios M. , Stavrinides Stavros G. , Hanias Michael P. , Papadopoulos Pericles , Matiadou Niki-Lina 

TITLE=Traces of tricritical dynamics beyond SSB in finite-size systems undergoing second-order phase transition: the case of the 3D Ising model

JOURNAL=Frontiers in Complex Systems

VOLUME=Volume 3 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/complex-systems/articles/10.3389/fcpxs.2025.1612998

DOI=10.3389/fcpxs.2025.1612998

ISSN=2813-6187

ABSTRACT=In finite-size thermal systems that exhibit second-order phase transition, the fluctuations of the order parameter ϕn obey type I intermittent dynamics at their pseudocritical temperature Tpc. Moreover, as recently demonstrated, spontaneous symmetry breaking (SSB) is gradually completed as temperature is reduced until reaching an SSB completion temperature, TSSB. Within this temperature zone, ϕn obey the dynamics of critical intermittency. This behavior has also been observed in pre-seismic fracture-induced electromagnetic emissions (FEME) of the MHz band—a real-world finite-size system undergoing a second-order phase transition. Interestingly, MHz FEME has recently been found to consistently present indications of tricritical dynamics after the SSB. We examine here whether this could also be true for a finite-size thermal system. We conduct a numerical experiment for the 3D Ising model at different temperatures by gradually reducing temperature beyond SSB and analyze order parameter fluctuations using the method of critical fluctuations (MCF) and a recently introduced wavelet-based method for detecting scaling behavior in noisy experimental data. Our results reveal that power-laws still exist within a very narrow zone of temperatures right after SSB completion for the 3D Ising model. These power-laws are shown to be compatible with another form of intermittency that determines the dynamics of the order parameter fluctuations close to the Griffiths tricritical point. As a possible interpretation of this finding, we suggest that our results imply that 3D Ising presents, just below TSSB, an imprint approaching the Griffiths tricritical point from the second-order phase transition line.