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Size effects in finite systems with long-range interactions

E. S. Loscar

C. M. Horowitz

  • Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP, CCT La Plata-CONICET, Calle 59 no. 789, B1900BTE La Plata, Argentina and Departamento de Física, Universidad Nacional de La Plata, c.c. 67, 1900 La Plata, Argentina

  • Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), UNLP, CCT La Plata-CONICET, Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina

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Phys. Rev. E 97, 032103 – Published 6 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032103

Abstract

Small systems consisting of particles interacting with long-range potentials exhibit enormous size effects. The Tsallis conjecture [Tsallis, Fractals 3, 541 (1995)], valid for translationally invariant systems with long-range interactions, states a well-known scaling relating different sizes. Here we propose to generalize this conjecture to systems with this symmetry broken, by adjusting one parameter that determines an effective distance to compute the strength of the interaction. We apply this proposal to the one-dimensional Ising model with ferromagnetic interactions that decay as 1/r1+σ in the region where the model has a finite critical temperature. We demonstrate the convenience of using this generalization to study finite-size effects, and we compare this approach with the finite-size scaling theory.

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References (47)

  1. Magnetic Properties of Fine Particles, edited by J. L. Dorman and D. Fiorani (North-Holland, Amsterdam, 1992).
  2. M. Kishimoto, Y. Sakurai, and T. Ajima, J. Appl. Phys. 76, 7506 (1994).
  3. R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, J. Phys.: Condens. Matter 26, 103202 (2014).
  4. C.-b. Rong, D. Li, V. Nandwana, N. Poudyal, Y. Ding, Z. L. Wang, H. Zeng, and J. P. Liu, Adv. Mater. 18, 2984 (2006).
  5. O. Hovorka, S. Devos, Q. Coopman, W. J. Fan, C. J. Aas, R. F. L. Evans, X. Chen, G. Ju, and R. W. Chantrell, Appl. Phys. Lett. 101, 052406 (2012).
  6. M. O. A. Ellis and R. W. Chantrell, Appl. Phys. Lett. 106, 162407 (2015).
  7. A. Lyberatos, D. Weller, G. J. Parker, and B. C. Stipe, J. Appl. Phys. 112, 113915 (2012).
  8. A. Lyberatos, D. Weller, and G. J. Parker, J. Appl. Phys. 114, 233904 (2013).
  9. R. H. French et al., Rev. Mod. Phys. 82, 1887 (2010).
  10. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1992).
  11. V. Privman (ed.), Finite-Size Scaling and Numerical Simulations of Statistical Systems (World Scientific, Singapore, 1990).
  12. K. Binder and D. Heermann, Monte Carlo Simulations in Statistical Physics: An Introduction, Fourth edition (Springer-Verlag, Berlin, Heidelberg, New York, 2002)
  13. J. G. Brankov, D. M. Dantchev, and N. S. Tonchev, The Theory of Critical Phenomena in Finite-Size Systems-Scaling and Quantum Effects (World Scientific, Singapore, 2000).
  14. D. M. Dantchev, H. W. Diehl, and D. Gruneberg, Phys. Rev. E 73, 016131 (2006).
  15. D. M. Dantchev, F. Schlesener, and S. Dietrich, Phys. Rev. E 76, 011121 (2007).
  16. G. Valchev and D. M. Dantchev, Phys. Rev. E 96, 022107 (2017).
  17. H. Chamati and N. S. Tonchev, Phys. Rev. E 63, 026103 (2001).
  18. H. Chamati and N. S. Tonchev, Mod. Phys. Lett. B 17, 1187 (2003).
  19. J. Wang, W. Wu, F. Zhao, and G.-m. Zhao, Appl. Phys. Lett. 98, 083107 (2011).
  20. X. Batlle and A. Labarta, J. Phys. D: Appl. Phys. 35, R15 (2002).
  21. C. Tsallis, Fractals 3, 541 (1995).
  22. P. Jund, S. G. Kim, and C. Tsallis, Phys. Rev. B 52, 50 (1995).
  23. R. F. S. Andrade and S. T. R. Pinho, Phys. Rev. E 71, 026126 (2005).
  24. D. Ruelle, Commun. Math. Phys. 9, 267 (1968).
  25. F. J. Dyson, Commun. Math. Phys. 12, 91 (1969).
  26. M. Ainzenman and R. Fernandez, Lett. Math. Phys. 16, 39 (1988).
  27. D. E. Rodriguez, M. A. Bab, and E. V. Albano, J. Stat. Mech. (2011) P090007.
  28. S. A. Cannas, C. M. Lapilli, and D. A. Stariolo, Int. J. Mod. Phys. C 15, 115 (2004).
  29. S. A. Cannas, Phys. Rev. B 52, 3034 (1995).
  30. S. A. Cannas and F. A. Tamarit, Phys. Rev. B 54, R12661 (1996).
  31. E. Luijten and H. W. J. Blöte, Phys. Rev. B 56, 8945 (1997).
  32. D. P. Landau, Phys. Rev. B 13, 2997 (1976).
  33. E. Flores-Sola, B. Berche, R. Kenna, and M. Weigel, Eur. Phys. J. B 88, 28 (2015).
  34. E. Flores-Sola, B. Berche, R. Kenna, and M. Weigel, Phys. Rev. Lett. 116, 115701 (2016).
  35. R. Kenna and B. Berche, Scaling and finite-size scaling above the upper critical dimension, in Order, Disorder, and Criticality: Advanced Problems of Phase Transition Theory, Vol. 4, edited by Yu. Holovatch (World Scientific, Singapore, 2015).
  36. M. E. Fisher, S. K. Ma, and B. G. Nickel, Phys. Rev. Lett. 29, 917 (1972).
  37. Z. Glumac and K. Uzelac, J. Phys. A: Math. Gen. 21, L421 (1988).
  38. Z. Glumac and K. Uzelac, J. Phys. A: Math. Gen. 22, 4439 (1989).
  39. Y. Tomita, J. Phys. Soc. Japan 78, 014002 (2009).
  40. E. Bayong, H. T. Diep, and T. T. Truong, J. Appl. Phys. 85, 6088 (1999).
  41. E. Bayong and H. T. Diep, Phys. Rev. B 59, 11919 (1999).
  42. C. Tsallis, Braz. J. Phys. 29, 1 (1999).
  43. L. A. del Pino, P. Troncoso, and S. Curilef, Phys. Rev. B 76, 172402 (2007).
  44. S. Curilef, Int. J. Mod. Phys. C 11, 629 (2000).
  45. S. Curilef, L. A. del Pino, and P. Orellana, Phys. Rev. B 72, 224410 (2005).
  46. R. Rüger and R. Valentí, Phys. Rev. B 86, 024431 (2012).
  47. K. Binder and E. Luijten, Phys. Rep. 344, 179 (2001).

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Phys. Rev. E 97, 032103– Published 6 March, 2018
  • Received 7 June 2017
  • Revised 23 December 2017
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