Calculation of relative variance of the magnetization and susceptibility in a disordered Ising model. Results of Monte Carlo simulation

A. B. Babaev ; A. K. Murtazaev

Matematičeskoe modelirovanie, Tome 30 (2018) no. 12, pp. 55-62.

Résumé

Based on the Monte Carlo method, the relative dispersions of the magnetization $R_m$ and the susceptibility $R_\chi$ in the disordered Ising model are calculated as a function of the degree of dilution of the disorder. It is shown, that the introduction of disorder in the form of nonmagnetic impurities in the three-dimensional Ising model leads to a nonzero values for $R_m$ and $R_\chi$ at the critical point.

Détail

Keywords: Ising model, disorder
Mots-clés : dispersion, Monte Carlo.

Bibliographie

[1] S. Wiseman, E. Domany, “Self-averaging, distribution of pseudocritical temperatures, and finite size scaling in critical disordered systems”, Phys. Rev. E, 58 (1998), 2938 | DOI

[2] S. Wiseman, E. Domany, “Finite-Size Scaling and Lack of Self-Averaging in Critical Disordered Systems”, Phys. Rev. Lett., 81 (1998), 22 | DOI

[3] A. Aharony, A.B. Harris, S. Wiseman, “Critical Disordered Systems with Constraints and the Inequality $v > 2/d$”, Phys. Rev. Lett., 81 (1998), 252 | DOI

[4] P.-E. Berche, Ch. Chatelain, B. Berche, W. Janke, “Bond dilution in the 3D Ising model: a Monte Carlo study”, European Physical J. B, 38 (2004), 463 | DOI

[5] M.I. Marques, J.A. Gonzalo, J. Iniguez, “Self-averaging of random and thermally disordered diluted Ising systems”, Phys. Rev. E, 60 (1999), 2394 | DOI

[6] M.I. Marques, J.A. Gonzalo, J. Iniguez, “Universality class of thermally diluted Ising systems at criticality”, Phys. Rev. E, 62 (2000), 191 | DOI

[7] V.V. Prudnikov, P.V. Prudnikov, A.A. Fedorenko, “Field-theory approach to critical behaviour of systems with long-range correlated defects”, Phys. Rev. B, 62 (2000), 8777 | DOI | MR

[8] A.Z. Patashinskii, V.A. Pokrovskii, Fluktuatsionnaia teoriia fazovykh perekhodov, Nauka, M., 1982, 223 pp.

[9] A.K. Murtazaev, A.B. Babaev, “Phase Transitions in the Two-Dimensional Ferro- and Anti-ferromagnetic Potts Models on a Triangular Lattice”, Journal of Experimental and Theoretical Physics, 115:6 (2012), 1042 | DOI

[10] A.K. Murtazaev, A.B. Babaev, G.Y. Aznaurova, “Investigation of the Critical Properties in the 3d Site-Diluted Potts Model”, Solid State Phenomena, 152–153 (2009), 571 | DOI

[11] A.K. Murtazaev, A.B. Babaev, G.Y. Aznaurova, “Phase Transitions in 3D Site-Diluted Potts Model with Spin States q=4”, Solid State Phenomena, 168–169 (2011), 357

[12] A.K. Murtazaev, A.B. Babaev, “Tricritical Point of the Three-Dimensional Potts Model (q=4) with Quenched Nonmagnetic Disorder”, JETP Letters, 99 (2014), 535 | DOI

[13] A.K. Murtazaev, I.K. Kamilov, A.B. Babaev, “Critical behavior of spin systems with quenched disorder”, J. of Magnetism and Magnetic Materials, 300 (2006), 538

[14] V.V. Prudnikov, P.V. Prudnikov, A.N. Vakilov, A.S. Krinitsyn, “Computer Simulation of the Critical Behavior of 3D Disordered Ising Model”, Journal of Experimental and Theoretical Physics, 105:2 (2007), 371 | DOI | MR

[15] V.S. Dotsenko, “Critical phenomena and quenched disorder”, Physics-Uspekhi, 38 (1995), 457 | DOI | DOI

[16] U. Wolff, “Collective Monte Carlo Updating for spin systems”, Phys. Rev. Lett., 62 (1989), 361 | DOI

[17] J.-S. Wang, R.H. Swendsen, “Cluster Monte Carlo algorithms”, Phys. A, 167 (1990), 565 | DOI | MR

[18] A.K. Murtazaev, A.B. Babaev, “Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model”, J. of Magnetism and Magnetic Materials, 324 (2012), 3870 | DOI

[19] A.B. Babaev, A.K. Murtazaev, “Computer simulation of the critical behavior in spin models with nonmagnetic impurities”, Low Temperature Physics, 41 (2015), 608 | DOI

[20] P. Peczak, A.M. Ferrenberg, D.P. Landau, “High-accuracy Monte Carlo study of the three-dimensional classical Heisenberg ferromagnet”, Phys. Rev. B, 43 (1991), 6087 | DOI

[21] O.A. Vasilyev, L.N. Shchur, “Universality of the Ratio of the Critical Amplitudes of the Magnetic Susceptibility in a Two-Dimensional Ising Model with Nonmagnetic Impurities”, Journal of Experimental and Theoretical Physics, 90:6 (2000), 964 | DOI