The search for intermittency in the finite-size Ising model

Z. Burda, K. Zalewski, R. Peschanski +1 more

Z. Burda, J. Wosiek, K. Zalewski

Yiannis Contoyiannis, Stelios M. Potirakis, Stavros G. Stavrinides +3 more

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.

Yiannis Contoyiannis

A numerical simulation using the chaotic Dynamics of intermittency at a finite size Z(3) spin system in a 3D lattice reveals: (a) the existence of a second order phase transition with a zone hysteresis characterized from resonances phenomena (b) An hybrid appearance of mean-field universality class and 3D Ising model universality class , all these inside the zone hysteresis (c) a weak first order phase transition through a tricritical crossover. So, a complicated behavior in Z(3) symmetry exists.

Ziya Merdan, Nida Aras, Cihan Kürkçü

Yoshihiro Nishiyama

Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as nu=0.6245(28) and y(h)=2.4709(73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.