Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Spin-Orbital States and Strong Antiferromagnetism of Layered Eu2SrFe2O6 and Sr3Fe2O4Cl2

The insulating iron compounds Eu₂SrFe₂O₆ and Sr₃Fe₂O₄Cl₂ have high-temperature antiferromagnetic (AF) order despite their different layered structures. Here, we carry out density functional calculations and Monte Carlo simulations to study their electronic structures and magnetic properties aided with analyses of the crystal field, magnetic anisotropy, and superexchange. We find that both compounds are Mott insulators and in the high-spin (HS) Fe²⁺ state (S = 2) accompanied by the weakened crystal field. Although they have different local coordination and crystal fields, the Fe²⁺ ions have the same level sequence and ground-state configuration (3z²-r²)²(xz, yz)²(xy)¹(x²-y²)¹. Then, the multiorbital superexchange produces strong AF couplings, and the (3z²-r²)/(xz, yz) mixing via the spin-orbit coupling (SOC) yields a small in-plane orbital moment and anisotropy. Indeed, by tracing a set of different spin-orbital states, our density functional calculations confirm the strong AF couplings and the easy planar magnetization for both compounds. Moreover, using the derived magnetic parameters, our Monte Carlo simulations give the Néel temperature T_N = 420 K (372 K) for the former (the latter), which well reproduce the experimental results. Therefore, the present study provides a unified picture for Eu₂SrFe₂O₆ and Sr₃Fe₂O₄Cl₂ concerning their electronic and magnetic properties.

Dynamic critical behavior of the two-dimensional Ising model with nonextensive statistics

The dynamic critical behavior of the two-dimensional Ising model with nonextensive Tsallis statistics has been studied. The values of the dynamic critical index z as well as the values of the indices ν and β for different values of the deformation parameter q have been obtained. The emergence of a new type of critical behavior has been revealed.

Generalized Metropolis dynamics with a generalized master equation: an approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature β. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q=1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q≠1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.