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

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.