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arXiv:1502.02924

The effect of the heating rate on the order to order phase transition

Aycan Özkan, Bülent Kutlu

Published Feb 10, 2015• 0 citations
arXivHTMLPDF

Abstract

The simple cubic spin-1 Ising (BEG) model exhibits the ferromagnetic (F) - ferromagnetic (F) phase transition at low temperature region for the interval 1.40
DOI
10.48550/arxiv.1502.02924

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The simple cubic spin-1 Ising model exhibits the ferromagnetic (F)–ferromagnetic (F) phase transition in the low temperature region for the interval 1.40 < d = D/J < 1.48 at k = K/J = –0.5. The degree of the F-F phase transition determines the special point on the (kBT/J, d) phase diagram. In this paper, the critical behavior of the F-F phase transition was investigated for different heating rates using the cellular automaton heating algorithm. The universality class and the type of F-F phase transition were analyzed using the finite-size scaling theory and the power law relations. The results show that the F-F phase transition may be the second order, the first order or the weak first order depending on the heating rate in the interval 1.40 < d < 1.48 for k = –0.5.
The fcc spin-1 Ising (BEG) model has a dense ferromagnetic (dfdfdf) ground state instead of the ferromagnetic ground state at low temperature region and exhibits the dense ferromagnetic (dfdfdf) - ferromagnetic (FFF) phase transition for d=D/J=2.9d=D/J=2.9d=D/J=2.9, k=K/J=−0.5k=K/J=-0.5k=K/J=−0.5, ℓ=L/J=0\ell =L/J=0ℓ=L/J=0 and h=H/J=0h=H/J=0h=H/J=0. The critical behavior of the dense ferromagnetic (dfdfdf) - ferromagnetic (FFF) phase transition has been investigated using the cellular automaton cooling and heating algorithms. The universality class and the type of the dense ferromagnetic (dfdfdf) - ferromagnetic (FFF) phase transition have been researched within the framework of the finite - size scaling, the power law relations and the probability distribution. The results show that the dense ferromagnetic- ferromagnetic phase transition is of the second order and the model shows universal second order Ising critical behavior at d=2.9d=2.9d=2.9 parameter value through k=−0.5k=-0.5k=−0.5 line.
A scheme for calculating the thermodynamic characteristics of a 3D one-component spin system in the temperature range below the critical temperature is described on the basis of the sextic measure density (ρ6 model) taking into account the first confluent correction. A microscopic analog of the Landau free energy is calculated. The coefficients of average spin moment, leading critical amplitudes, and the amplitudes of the confluent correction to specific heat and susceptibility of the system are calculated for different values of effective radius of the exponentially decreasing interaction potential. Plots of temperature dependence of entropy and other thermodynamic characteristics in the vicinity of Tc are given for various values of effective radius. The variation of the free energy of the system at the phase transition point, average spin moment, and specific heat with increasing ratio of the potential effective radius to the constant of a simple cubic lattice is traced. The results of calculations and their comparison with the data obtained by other authors show that the ρ6 model provides a better quantitative description of the critical behavior of a 3D Ising ferromagnet than the ρ4 model.