The relativistic effect of critical temperature reduction in the two dimensional Ising model / O efeito relativístico da redução crítica de temperatura no modelo bidimensional de Ising

Rafael Santos da Costa, Jair Rodrigues Neyra, Maria Liduína das Chagas, Maria das Graças Dias da Silva, Thiago Crisóstomo Carlos Nunes, Thiago Rafael da Silva Moura


We investigated the impact of Kaniadakis statistics on thermodynamic properties for a square magnetic grid. We used the Ising model. We reported numerical results for a two-dimensional magnetic network in a thermal bath. We calculated the probabilities of transition between states using -statistics, the Metropolis dynamics for stochastic processes of the finite-sized magnetic network, considering that the system interacts with a thermal reservoir. We investigated the behavior of various thermodynamic properties. We observed typical measurements of magnetization, energy and specific heat. Increasing the  parameter reduces the critical temperature. We observed by the measurements of the fourth order Binder cumulative of magnetization, that for different network sizes and different values of the parameter , the system transition temperature magnetic decreases as κ increases.



κ-exponential, Ising model, phase transitions.

Texto completo:



Slonczewski, J.C. (1989). Phys. Rev. B 39, 6995.

Mattis, D.C. (1981) “The Theory of Magnetism I.” Springer Verlag, Berlin.

Gerlach, W. and Stern, O. (1992). Z. Phys. 9, 349.

Lodder, J.C. (2006) “Patterned Nanomagnetic Films”, in: D.J. Sellmyer and R. Skomski (eds), Advanced Magnetic Materials Nanostructures, Springer, Berlin, pp.261-293.

AJAYAN, P.M. Nanotubes from carbo. Chem. Rev., Washington DC, v.99, n.7, 1999.

BAIBICH, M. N.; BROTO, J. M.; FERT, A.; VAN DAU, F. Nguyen; PETROFF, F.; EITENNE, P.; CREUZET, G.; FRIEDERICH, A. and CHAZELAS, J. . Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices. Physical Review Letters. v.61, .21, 1988.

BINASCH, G.; GRÜNBERG, P.; SAURENCH, F. and ZINN, W. . Enhanced magnetoresistance in layered magnetic structures with antiferomagnetic interlayer exchange. Physical Review B. v.39, n.7, 1989.

SHINJO, T. Nanomagnetism and Spintronics. 1st ed. Amsterdã: Elsevier, 2009.

TSALLIS, C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys., v. 52, p. 470, 1988.

KANIADAKIS, G. Non-linear kinetics underlying generalized statistics. Physica A, v. 256, p. 405–425, 2001.

KANIADAKIS, G. Statistical mechanics in the context of special relativity. Phys. Rev.E, v. 66, p. 56125, 2002.

KANIADAKIS, G. Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions. Entropy, v. 15, n. 10, p. 3983–4010, 2013.

N.Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, Journal of Chemical Physics 21, 1087, 1953.

NEWMAN, M. E. J.; BARKEMA, G. T. Monte Carlo Methods in Statistical Physics. [S.l.]: Oxford University Press Inc, New York, 1999.

TSAI, S.; SALINAS, S. R. A. Fourth-order cumulants to characterize the phase transitions of a spin-1 ising model. Braz. J. Phys., v. 28, n. 1, 1998.



  • Não há apontamentos.