Magnetic phase diagram for a nonextensive system: Experimental connection with manganites

Abstract

In the present paper we make a thorough analysis of a classical spin system, within the framework of Tsallis nonextensive statistics. From the analysis of the generalized Gibbs free energy, within the mean-field approximation, a paramagnetic-ferromagnetic phase diagram, which exhibits first-and second-order phase transitions, is built. The features of the generalized and classical magnetic moment are mainly determined by the values of q, the nonextensive parameter. The model is successfully applied to the case of La 0.60 Y 0.07 Ca 0.33 MnO 3 manganite. The temperature and magnetic field dependence of the experimental magnetization on this manganite are faithfully reproduced. The agreement between rather ''exotic'' magnetic properties of manganites and the predictions of the q statistics comes to support our initial claim that these materials are magnetically nonextensive objects.

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

“…The relation between these parameters is given in Eq.(4). The advantage of our approach over previous one, for the choice of the temperature scale, is that ours is supported by previous description of the magnetic properties, experimentally and theoretically investigated, of manganites [6,7,17,18,19]. Thus, based on that, we believe that the 2D Ising model undergoes a phase transition even for q = 1.0, and the scaling relations should be changed as described above.…”

“…The Monte Carlo simulation of an Ising model with nearest-neighbors interactions showed a distinct behavior of the same system considered in the infinite-range-interaction limit [19]. Jumps on the magnetization and susceptibility curves in the range 0.0 < q < 0.5 occur in both approaches, but for short-range interactions we do not have first-order phase transitions.…”

“…In our approach, different from other authors [25,26,38,39,40], we simply changed the weight in the Metropolis algorithm to a ratio between the escort probabilities of the nonextensive statistics. This study was motivated by possible connection of the Tsallis statistics and some manganese oxides, called manganites, like La 0.60 Y 0.07 Ca 0.33 MnO 3 [6,17,18,19]. Due to computational cost, our simulations were done after 10 7 Monte Carlo steps, with the entropic index q ∈ [0, 1] and the linear lattice sizes L = 32, 64, 128, 256 and 512.…”

“…From a pragmatic point of view, since (β ′ q ) −1 has the dimension of energy, (β ′ q k) −1 is a temperature scale which can be used to interpret experimental results. The validity of this choice was first shown experimentally [18], and later theoretically [6,7,17,19] for manganites.…”

“…More recently, some works have investigated the magnetic properties of some manganese oxides, called manganites, and connections with the nonextensive statistics have been proposed [6,17,18,19]. In a recent work, Reis et al [19] studied the phase transitions that occur in a classical spin system within the mean-field approximation, in the framework of Tsallis nonextensive statistics, and some interesting properties were found: the system presents first-order phase transitions for q < 0.5, but only continuous transitions were found for 0.5 < q < 1.0. The results present qualitative agreement with experimental data in the La 0.60 Y 0.07 Ca 0.33 MnO 3 manganite [20].…”