On the equivalence of different order parameters for Ising ferromagnets

C. Gruber, Joel L. Lebowitz

Norman E. Frankel

Fateme Izadi, Reza Sepehrinia

We study the competition between ferromagnetic and spin glass phases using a system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We obtain the replica-symmetric solution for the free energy of this system in terms of magnetization and Edwards-Anderson order parameters in both subsystems. Using these order parameters we are able to identify different phases in the system and determine which phase is dominant for different strengths of the coupling between two subsystems. We observe that both subsystems are in the same phase although with different order parameters. The phase boundary between paramagnetic-ferromagnetic and paramagnetic--spin glass phases is more or less similar to that in the Sherrington-Kirkpatrick phase diagram. But the boundary between ferromagnetic--spin glass phases becomes qualitatively different as the coupling between the two subsystems changes. Remarkably, for intermediate values of the coupling, this phase boundary is such that there could be a reentrant transition between spin glass and ferromagnetic phases by increasing the temperature. We found that for some range of the coupling, the second-order transition between these phases turns into first order at a tricritical point. Further, we carry out the stability analysis by considering deviations from the replica-symmetric solution.

Ajay Halder, Muktish Acharyya

The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (pinned) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth-order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes (L). From the finite size analysis of dynamic order parameter and the dynamic susceptibility , we have estimated the critical exponents and (measured from the data read at the critical temperature obtained from Binder cumulant), and (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where and ), within the limits of statistical errors.

Ryuzo Abe

Vanja Marić, Florent Ferro, Maurizio Fagotti

When matter in different phases is brought into contact, an interface with unexpected properties can emerge. In the transverse-field Ising chain, the authors investigate the interface formed by joining a disordered state with a ferromagnetically ordered one. They show that, within this emergent region, order parameters and entanglement asymmetries of subsystems exhibit universal behavior. Correlations extend across the entire region, and the Wigner--Yanase skew information of large subsystems reveals macroscopic multipartite entanglement.