Nonequilibrium model on Archimedean lattices

• Authors: F. Lima
• Languages of publication: EN

Abstracts

EN

On (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T
c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T
c = 0.651(3) and U
4* = 0.612(5), and T
c = 0.667(2) and U
4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.

Keywords

EN

Monte Carlo simulation; critical exponents; phase transition; non-equilibrium

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 3
• Pages: 185-191

Dates

published

1 - 3 - 2014

online

13 - 3 - 2014

Contributors

author

F. Lima

• Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64.049-550, Teresina, Piauí, Brazil

References

• [1] S. Galam, J. Math. Psychol. 30, 426 (1986) http://dx.doi.org/10.1016/0022-2496(86)90019-2[Crossref]
• [2] S. Galam, J. Stat. Phys. 61, 943 (1990) http://dx.doi.org/10.1007/BF01027314[Crossref]
• [3] S. Fortunato, M. Macy, S. Redner, Editorial, J. Stat. Phys. 151, 1 (2013) http://dx.doi.org/10.1007/s10955-013-0703-2[Crossref]
• [4] S. Galam, J. Stat. Phys. 151, 46 (2013) http://dx.doi.org/10.1007/s10955-012-0641-4[Crossref]
• [5] S. Galam, Physica A 336, 49 (2004) http://dx.doi.org/10.1016/j.physa.2004.01.009[Crossref]
• [6] D. Stauffer, J. Stat. Phys. 151, 9 (2013) http://dx.doi.org/10.1007/s10955-012-0604-9[Crossref]
• [7] S. Galam, Sociophysics: A Physicist’s Modeling of Psycho-political Phenomena (Springer, Berlin, 2012) http://dx.doi.org/10.1007/978-1-4614-2032-3[Crossref]
• [8] M. J. de Oliveira, J. Stat. Phys. 66, 273 (1992) http://dx.doi.org/10.1007/BF01060069[Crossref]
• [9] M. A. Santos, S. Teixeira, J. Stat. Phys. 78, 963 (1995) http://dx.doi.org/10.1007/BF02183696[Crossref]
• [10] L. Crochik, T. Tomé, Phys. Rev. E 72, 057103 (2005) http://dx.doi.org/10.1103/PhysRevE.72.057103[Crossref]
• [11] W. Lenz, Z. Phys. 21, 613 (1920)
• [12] E. Ising, Z. Phys. 31, 253 (1925) http://dx.doi.org/10.1007/BF02980577[Crossref]
• [13] M. Hasenbusch, Int. J. Mod. Phys. C 12, 911 (2001) http://dx.doi.org/10.1142/S0129183101002383[Crossref]
• [14] J. J. Binney, N. J. Dowrick, A. J. Fisher, M. E. J. Newman, A theory of critical phenomena. An Introduction to the renormalization group (Clarendon Press, Oxford, 1992)
• [15] G. Grinstein, C. Jayaprakash, Y. He, Phys. Rev. Lett. 55, 2527 (1985) http://dx.doi.org/10.1103/PhysRevLett.55.2527[Crossref]
• [16] P. R. Campos, V. M. Oliveira, F. G. B. Moreira, Phys. Rev. E 67, 026104 (2003) http://dx.doi.org/10.1103/PhysRevE.67.026104[Crossref]
• [17] E. M. S. Luz, F. W. S. Lima, Int. J. Mod. Phys. C 18, 1251 (2007) http://dx.doi.org/10.1142/S0129183107011297[Crossref]
• [18] L. F. C. Pereira, F. G. B. Moreira, Phys. Rev. E 71, 016123 (2005) http://dx.doi.org/10.1103/PhysRevE.71.016123[Crossref]
• [19] F. W. S. Lima, A. O. Sousa, M. A. Sumour, Physica A 387, 3503 (2008) http://dx.doi.org/10.1016/j.physa.2008.01.120[Crossref]
• [20] F. W. S. Lima, U. L. Fulco, R. N. C. Filho, Phys. Rev. E 71, 036105 (2005) http://dx.doi.org/10.1103/PhysRevE.71.036105[Crossref]
• [21] F. W. S. Lima, Int. J. Mod. Phys. C 17, 1257 (2006) http://dx.doi.org/10.1142/S0129183106008972[Crossref]
• [22] F. W. S. Lima, A. A. Moreira, A. D. Araújo, Phys. Rev. E 86, 056109 (2012) http://dx.doi.org/10.1103/PhysRevE.86.056109[Crossref]
• [23] F. W. S. Lima, Commun. Comput. Phys. 2, 358 (2007)
• [24] A. D. Sánchez, J. M. Lopes, M. A. Rodriguez, Phys. Rev. Lett. 88, 048701 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.048701[Crossref]
• [25] P. Erdős, A. Rényi, Publ. Math. 6, 290 (1959)
• [26] P. Erdős, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960)
• [27] F. W. S. Lima, J. E. Moreira, J. S. Andrade, Jr., U. M. S. Costa, Physica A 283, 100 (2000) http://dx.doi.org/10.1016/S0378-4371(00)00134-5[Crossref]
• [28] F. W. S. Lima, U. M. S. Costa, M. P. Almeida, J. S. Andrade, Jr., Eur. Phys. J. B 17, 111 (2000) http://dx.doi.org/10.1007/s100510070165[Crossref]
• [29] A.-L. Barabási, R. Albert, Science 286, 509 (1999) http://dx.doi.org/10.1126/science.286.5439.509[Crossref]
• [30] A. Aleksiejuk, J. A. Hołyst, D. Stauffer, Physica A 310, 260 (2002) http://dx.doi.org/10.1016/S0378-4371(02)00740-9[Crossref]
• [31] F. W. S. Lima, K. Malarz, Int. J. Mod. Phys. C 17, 1273 (2006) http://dx.doi.org/10.1142/S0129183106009849[Crossref]
• [32] J. C. Santos, F. W. S. Lima, K. Malarz, Physica A 390, 359 (2011) http://dx.doi.org/10.1016/j.physa.2010.08.054[Crossref]
• [33] J.-S. Yang, I.-M. Kim, Phys. Rev. E 77, 051122 (2008) http://dx.doi.org/10.1103/PhysRevE.77.051122[Crossref]
• [34] Z.-X. Wu, P. Holme, Phys. Rev. E 81, 011133 (2010) http://dx.doi.org/10.1103/PhysRevE.81.011133[Crossref]
• [35] P. N. Suding, R. M. Ziff, Phys. Rev. E 60, 275 (1999) http://dx.doi.org/10.1103/PhysRevE.60.275[Crossref]
• [36] K. Malarz, M. Zborek, B. Wróbel, TASK Quarterly 9, 475 (2005)
• [37] W. Kwak, J.-S. Yang, J.-I. Shon, I.-M. Kim, Phys. Rev. E 75, 061110 (2007) http://dx.doi.org/10.1103/PhysRevE.75.061110[Crossref]
• [38] K. Binder, D. W. Heermann, Monte Carlo Simulation in Statistical Physics (Springer Verlag, Berlin and Heidelberg, 1988) http://dx.doi.org/10.1007/978-3-662-08854-8[Crossref]
• [39] R. Albert, A.-L. Barabási, Rev. Mod. Phys. 286, 47 (2002) http://dx.doi.org/10.1103/RevModPhys.74.47[Crossref]
• [40] S. N. Dorogovtsev, J. F. F. Mendes, Adv. Phys. 51, 1079 (2002) http://dx.doi.org/10.1080/00018730110112519[Crossref]
• [41] M. E. J. Newman, SIAM Rev. 45, 167 (2003) http://dx.doi.org/10.1137/S003614450342480[Crossref]

Identifiers

DOI

10.2478/s11534-014-0435-1