The $\pm J$ distribution in the mixed spin-$1/2$ and $5/2$

E. Albayrak   ; F. Ş. Özcan

Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 3, pp. 486-499

Résumé

Phase diagrams of the mixed spin-$1/2$ and $5/2$ Blume–Capel model on the Bethe lattice in the $\pm J$ distribution with probabilities $p$ and $1-p$ for $J>0$ and $J<0$ and the adjustment parameter $\alpha$ are obtained on the $(\alpha,T)$ and $(p, T)$ planes for given values of single-ion anisotropy $D$ by varying $p$ in the range $0\leq p\leq 1$ and $\alpha$ in the range $0\leq\alpha\leq 1$. The phase diagrams are constructed by studying the thermal variations of the order parameters in terms of exact recursion relations, and the probability distribution is then implemented into the model. The model presents first- and second-order phase transitions in addition to the tricritical and bicritical points for the coordination number $q=3$ corresponding to the honeycomb lattice.

Détail

Keywords: bilinear exchange interaction, Blume–Capel model, Bethe lattice, recursion relation, mixed-spin, phase diagram.

Bibliographie

[1] A. Albino Jr., F. D. Nobre, F. A. da Costa, “The spin-1 Ising spin glass: a renormalization-group approach”, J. Phys.: Condens. Matter, 12:26 (2000), 5713–5726 | DOI

[2] E. Albayrak, M. Karimou, “The $\pm J$ model for the mixed-spin $1/2$ and $5/2$ system”, Chinese J. Phys., 55:4 (2017), 1361–1368 | DOI

[3] Y. Miyoshi, T. Iwashita, T. Idogaki, “The three-dimensional $\pm J$ Ising model with uniform biquadratic exchange interaction”, J. Magn. Magn. Mater., 226–230, Part I (2001), 608–609 | DOI

[4] Y. Miyoshi, T. Idogaki, “Non-equilibrium relaxation study of the $\pm J$ Ising model with biquadratic exchange interaction”, J. Magn. Magn. Mater., 248:2 (2002), 318–331 | DOI

[5] S. L. Yan, L. L. Deng, “Thermodynamic properties of bond dilution Blume–Capel model with random crystal field”, Phys. A: Stat. Mech. Appl., 308:1–4 (2002), 301–312 | DOI

[6] H.-X. Zhu, S.-L. Yan, “Ferromagnetic properties of bond-dilution and random positive or negative uniaxial anisotropy Blume–Capel model”, Commun. Theor. Phys., 42:5 (2004), 789–794 | DOI

[7] S.-L. Yan, H.-X. Zhu, “Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume–Capel model in the presence of an applied field”, Chinese Phys., 15:12 (2006), 3026–3032 | DOI

[8] Ü. Akinci, Y. Yüksel, H. Polat, “Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice”, Phys. A: Stat. Mech. Appl., 390:4 (2011), 541–552 | DOI

[9] D. Peña, “Modelo de Blume–Emery–Griffiths de vidrio de espín”, Revista Colombiana de Física, 44:1 (2012), 87–91

[10] E. Albayrak, F. Ş. Özcan, “Mixed spin-$1/2$ and $5/2$ Blume–Capel model on the Bethe lattice in the $\pm J$ distribution with an adjusting parameter”, J. Supercond. Nov. Magn., 33:7 (2020), 2179–2188 | DOI

[11] E. Albayrak, “The spin-1 Blume–Capel model on the Bethe lattice in $\pm J$ distribution with an adjustable parameter between FM and AFM phases”, Chinese J. Phys., 56:2 (2018), 622–629 | DOI

[12] D. Peña Lara, J. E. Diosa, C. A. Lozano, “Blume–Capel spin-glass model for Fe–Mn–Al alloys”, Phys. Rev. E, 87:3 (2013), 032108, 9 pp. | DOI

[13] A. Yigit, E. Albayrak, “The random $J$-Model with biquadratic interaction”, J. Supercond. Nov. Magn., 29:9 (2016), 2535–2541 | DOI

[14] W. F. Wolff, J. Zittartz, “On the phase transition of the random bond Ising model”, Z. Phys. B, 52:2 (1983), 117–126 | DOI

[15] J. D. Reger, A. Zippelius, “Three-dimensional random-bond Ising model: Phase diagram and critical properties”, Phys. Rev. Lett., 57:25 (1986), 3225–3228 | DOI

[16] N. Benayad, A. Benyoussef, N. Boccara, “Re-entrant ferromagnetism in a two-dimensional Ising model with random nearest-neighbour interactions”, J. Phys. C: Solid State Phys., 21:31 (1988), 5417–5426 | DOI

[17] A. L. Talapov, L. N. Shchur, “The critical region of the random-bond Ising model”, J. Phys.: Condens. Matter, 6:40 (1994), 8295–8308 | DOI

[18] J.-S. Wang, W. Selke, Vl. S. Dotsenko, V. B. Andreichenko, “The two-dimensional random bond Ising model at criticality – a Monte Carlo study”, Europhys. Lett., 11:4 (1990), 301–306 | DOI

[19] F. D. Nobre, “The two-dimensional $\pm J$ Ising spin glass: a model at its lower critical dimension”, Phys. A: Stat. Mech. Appl., 319 (2003), 362–370 | DOI

[20] I. A. Gruzberg, N. Read, A. W. W. Ludwig, “Random-bond Ising model in two dimensions: The Nishimori line and supersymmetry”, Phys. Rev. B, 63:10 (2001), 104422, 27 pp. | DOI

[21] S. L. A. de Queiroz, “Multicritical point of Ising spin glasses on triangular and honeycomb lattices”, Phys. Rev. B, 73:6 (2006), 064410, 7 pp. | DOI

[22] W. Xiong, F. Zhong, W. Yuan, S. Fan, “Critical behavior of a three-dimensional random-bond Ising model using finite-time scaling with extensive Monte Carlo renormalization-group method”, Phys. Rev. B, 81:5 (2010), 051132, 10 pp. | DOI

[23] T. Papakonstantinou, A. Malakis, “Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line”, Phys. Rev. E, 87:1 (2013), 012132, 10 pp. | DOI

[24] S. Cho, M. P. A. Fisher, “Criticality in the two-dimensional random-bond Ising model”, Phys. Rev. B, 55:2 (1997), 1025–1031 | DOI

[25] K. Afif, A. Benyoussef, M. Hamedoun, A. Hourmatallah, “Phase diagram of $\mathrm{ZnCr}_{2p}\mathrm{Al}_{2-2p}\mathrm{S}_4$ and $\mathrm{Zn}_{1-p}\mathrm{Cd}_p\mathrm{Cr}_2\mathrm{Se}_4$”, Phys. Stat. Sol. (a), 171:2 (1999), 571–575 | 3.0.CO;2-O class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[26] R. F. S. Andrade, S. R. Salinas, “Diluted Ising model with competing interactions”, Phys. A: Stat. Mech. Appl., 270:3–4 (1999), 342–352 | DOI

[27] S. Boettcher, J. Davidheiser, “Reduction of dilute Ising spin glasses”, Phys. Rev. B, 77:21 (2008), 214432, 9 pp. | DOI

[28] J. R. de Sousa, D. F. de Albuquerque, I. P. Fittipaldi, “Spin-glass phase for the diluted site-bond-correlated version”, J. Magn. Magn. Mater., 149:3 (1995), 269–272 | DOI

[29] I. A. Hadjiagapiou, “Monte Carlo analysis of the critical properties of the two-dimensional randomly bond-diluted Ising model via Wang–Landau algorithm”, Phys. A: Stat. Mech. Appl., 390:7 (2011), 1279–1288 | DOI

[30] M. Serva, “Exact and approximate solutions for the dilute Ising model”, Phys. A: Stat. Mech. Appl., 390:13 (2011), 2443–2451 | DOI | MR

[31] G. R. Schreiber, “Frustrated Blume–Emery–Griffiths model”, Eur. Phys. J. B, 9:3 (1999), 479–490 | DOI

[32] M. Hasenbusch, A. Pelissetto, E. Vicari, “Critical behavior of three-dimensional Ising spin glass models”, Phys. Rev. B, 78:21 (2008), 214205, 23 pp. | DOI

[33] F. Romá, S. Risau-Gusman, A. J. Ramirez-Pastor, F. Nieto, E. E. Vogel, “The ground state energy of the Edwards–Anderson spin glass model with a parallel tempering Monte Carlo algorithm”, Phys. A: Stat. Mech. Appl., 388:14 (2009), 2821–2838 | DOI

[34] Y. Matsuda, M. Müller, H. Nishimori, T. Obuchi, A. Scardicchio, “Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice”, J. Phys. A: Math. Theor., 43:28 (2010), 285002, 20 pp. | DOI | MR

[35] G. Ceccarelli, A. Pelissetto, E. Vicari, “Ferromagnetic-glassy transitions in three-dimensional Ising spin glasses”, Phys. Rev. B, 84:13 (2011), 134202, 9 pp. | DOI

[36] E. Albayrak, “$\pm J$ model on the Bethe lattice with crystal field interaction”, J. Magn. Magn. Mater., 355 (2014), 18–21 | DOI

[37] D. F. de Albuquerque, I. P. Fittipaldi, J. R. de Sousa, “Site-bond correlations in the three-dimensional Heisenberg model: Application to $\mathrm{KNi}_p\mathrm{Mg}_{1-p}\mathrm{F}_3$”, Phys. Rev. B, 56:21 (1997), 13650–13653 | DOI

[38] Y. El Amraoui, L. Bejjit, A. Lamrabat, H. Arhchoui, A. Benyoussef, M. Haddad, “The antiferromagnetic exchange interaction anisotropy and magnetic properties of a diluted Ising-72 model”, J. Magn. Magn. Mater., 241:2–3 (2002), 371–380 | DOI

[39] J. Kple, F. Hontinfinde, E. Albayrak, “Staggered quadrupolar phase in the bond-diluted spin-1 Blume–Emery–Griffiths model”, Internat. J. Theor. Phys., 59:12 (2020), 3915–3935 | DOI | MR

[40] N. Benayad, A. Klümper, J. Zittartz, A. Benyoussef, “Two-dimensional mixed spin Ising models with bond dilution and random $\pm J$ interactions”, Z. Phys. B, 77:2 (1989), 339–341 | DOI

[41] Y. Belmamoun, M. Kerouad, “Phase transition and magnetic properties of a bond-diluted mixed spin-1 and spin-$\frac{1}{2}$ Ising model with the uniaxial and biaxial single-ion anisotropy”, Phys. Scr., 77:2 (2008), 025706, 8 pp. | DOI

[42] Y. F. Zhang, S. L. Yan, “Critical behaviors and magnetic multi-compensation points of bond dilution mixed Blume–Capel model in bimodal magnetic field”, Sol. State Commun., 146:11–12 (2008), 478–482 | DOI

[43] N. Benayad, A. Dakhama, A. Klümper, J. Zittartz, “Mixed spin-$3/2$ and spin-$1/2$ Ising models with random nearest-neighbour interactions”, Ann. Phys. Lpz., 508:4 (1996), 387–400 | DOI

[44] E. Albayrak, “The $\pm J$ model for the mixed-spin $1/2$ and $3/2$ Blume–Capel model”, Phys. B: Condens. Matt., 494 (2016), 91–95 | DOI | MR

[45] M. Karimou, R. A. Yessoufou, A. Kpadonou, T. Oke, F. Hontinfinde, “Bethe approach study of the mixed spin-$1/2$ and spin-$5/2$ Ising system in the presence of an applied magnetic field”, Condens. Matter Phys., 19:3 (2016), 33003, 22 pp. | DOI