Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group — Oak Academic Publishing
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Phase Diagrams of the Semi-Infinite Blume-Capel Model with Mixed Spins (SA = 1 and SB = 3/2) by Migdal Kadanoff Renormalization Group
Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
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Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
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Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
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Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, UniversitéChouaib Doukkali, El Jadida, Maroc
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Département de Physique-Chimie, CRMEF El Jadida-Safi, Safi, Maroc
1 Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
2 Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
3 Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, Université Chouaib Doukkali, El Jadida, Maroc
4 Laboratoire L.P.M.C., Equipe de Physique théorique, Faculté des Sciences, UniversitéChouaib Doukkali, El Jadida, Maroc
5 Département de Physique-Chimie, CRMEF El Jadida-Safi, Safi, Maroc
We study the mixed spin-1 and spin-3/2 Blume-Capel model under crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal-Kadanoff technique. As a function of the ratio R of bulk and surface interactions and the ratios R 1 and R 2 of bulk and surface crystals fields on the spin-1 and spin-3/2 respectively, we have determined various types of phase diagrams. Besides second- order transition lines, first-order phase transition lines terminating at tricritical points are obtained. We found that there existed nine main types of phase diagram showing a variety of phase transitions associated with the surface, including ordinary, extraordinary, surface and special phase transitions.
Binder, K. (1983) Critical Behavior at Surfaces. In: Domb, C. and Lebowitz, J., Eds., Phase Transitions and Critical Phenomena, Vol. 8, Academic Press, New York, 1-444.
Diehl, H.W. (1986) Field-Theoretical Approach to Critical Behaviour at Surfaces. In: Domb, C. and Lebowitz, J.L., Eds., Phase Transition and Critical Phenomena, Vol. 10, Academic Press, London, 75-267.
Diehl, H.W. (1997) The Theory of Boundary Critical Phenomena. International Journal of Modern Physics B, 11, 3503. http://dx.doi.org/10.1142/S0217979297001751
Binder, K. and Hohenberg, P.C. (1974) Surface Effects on Magnetic Phase Transitions. Physical Review B, 9, 2194.
Rau, C. and Robert, M. (1987) Surface Magnetization of Gd at the Bulk Curie Temperature. Physical Review Letters, 58, 2714.
Tang, H., Weller, D., Walker, T.G., Scott, J.C., Chappert, C., Hopster, H., Pang, A.W., Dessau, D.S. and Pappas, D.P. (1993) Magnetic Reconstruction of the Gd(0001) Surface. Physical Review Letters, 71, 444.
Gimbert, F., Calmels, L. and Andrieu, S. (2011) Localized Electron States and Spin Polarization in Co/Ni (111) Overlayers Physical Review, 84, Article ID: 094432.
Arnold, C.S. and Pappas, D.P. (2000) Gd(0001): A Semi-Infinite Three-Dimensional Heisenberg Ferromagnet with Ordinary Surface Transition. Physical Review Letters, 85, 5202.
Prinz, G.A. (1998) Magnetoelectronics. Science, 282, 1660. http://dx.doi.org/10.1126/science.282.5394.1660
Monsuripur, M. (1987) Magnetization Reversal, Coercivity, and the Process of Thermomagnetic Recording in Thin Films of Amorphous Rare Earth-Transition Metal Alloys. Journal of Applied Physics, 61, 1580. http://dx.doi.org/10.1063/1.338094
Hasenbusch, M. (2011) A Monte Carlo Study of Surface Critical Phenomena: The Special Point. Physical Review B, 84, Article ID: 134405.
Eisenriegler, E. and Diehl, H.W. (1988) Surface Critical Behavior of Tricritical Systems. Physical Review B, 37, 5257-5273.
Bray, A.J. and Moore, M.A. (1977) Critical Behaviour of Semi-Infinite Systems. Journal of Physics A: Mathematical and General, 10, No. 11. http://dx.doi.org/10.1088/0305-4470/10/11/021
Lubensky, T.C. and Rubin, M.H. (1975) Critical Phenomena in Semi-Infinite Systems: I. ε Expansion for Positive Extrapolation Length. Physical Review B, 11, 4533.
Lubensky, T.C. and Rubin, M.H. (1975) Critical Phenomena in Semi-Infinite Systems: II. Mean-Field Theory. Physical Review B, 12, 3885.
Diehl, H.W. and Dietrich, S. (1981) Field-Theoretical Approach to Static Critical Phenomena in Semi-Infinite Systems. Zeitschrift für Physik B Condensed Matter, 42, 65-86. http://dx.doi.org/10.1007/BF01298293
Diehl, H.W., Dietrich, S. and Eisenriegler, E. (1983) Universality, Irrelevant Surface Operators and Corrections to Scaling in Systems with Free Surfaces and Defect Planes. Physical Review B, 27, 2937.
Diehl, H.W. and Shpot, M. (1998) Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems. Nuclear Physics B, 528, 595-647. http://dx.doi.org/10.1016/S0550-3213(98)00489-1
Diehl, H.W. and Nusser, A. (1990) Critical Behavior at Dirty Surfaces. Zeitschrift für Physik B Condensed Matter, 79, 79-90. http://dx.doi.org/10.1007/BF01387828
Usatenko, Z.E., Shpot, M.A. and Hu, C.-K. (2001) Surface Critical Behavior of Random Systems: Ordinary Transition. Physical Review E, 63, Article ID: 056102.
Au-Yang, H. (1973) Thermodynamics of an Anisotropic Boundary of a Two-Dimensional Ising Model. Journal of Mathematical Physics, 14, 937. http://dx.doi.org/10.1063/1.1666420
Fisher, M.E. and Caginalp, G. (1977) Wall and Boundary Free Energies. Communications in Mathematical Physics, 56, 11-56. http://dx.doi.org/10.1007/BF01611116
Reedm P. (1978) Correlation near the Free Surface of an Ising Ferromagnet. Journal of Physics A: Mathematical and General, 11, 137. http://dx.doi.org/10.1088/0305-4470/11/1/015
Au-Yang, H. and Fisherm M.E. (1980) Wall Effects in Critical Systems: Scaling in Ising Model Strips. Physical Review B, 21, 3956. http://dx.doi.org/10.1103/PhysRevB.21.3956
Albano, E.V. and Binder, K. (2012) Wetting Transition in the Two-Dimensional Blume-Capel Model: A Monte Carlo Study. Physical Review E, 85, Article ID: 061601. http://dx.doi.org/10.1103/PhysRevE.85.061601
Dietrich, S. (1988) Wetting Phenomena in Phase Transitions and Critical Phenomena. In: Domb, C. and Lebowitz, J.L., Eds., Phase Transitions and Critical Phenomena, Vol. 12, Academic, London, 1-218.
Benyoussef, A., Boccara, N. and Saber, M. (1986) Three-Dimensional Semi-Infinite Spin-1 Ising Model Interaction with Crystal Field. Journal of Physics C: Solid State Physics, 19, 1983. http://dx.doi.org/10.1088/0022-3719/19/12/012
Blume, M. (1966) Theory of the First-Order Magnetic Phase Change in U O 2. Physical Review, 141, 517-524. http://dx.doi.org/10.1103/PhysRev.141.517
Capel, H.W. (1966) On the Possibility of First-Order Phase Transitions in Ising Systems of Triplet Ions with Zero-Field Splitting. Physica, 32, 966-988. http://dx.doi.org/10.1016/0031-8914(66)90027-9
Bakchich, A. and El Bouziani, M. (1999) The Semi-Infinite Spin-3/2 Blume-Capel Model. Journal of Physics: Condensed Matter, 11, 6147. http://dx.doi.org/10.1088/0953-8984/11/32/306
Khan, O. (1993) Molecular Magnetism, VCH, New York.
Benayad, N. and Zittartz, J. (1990) Real-Space Renormalization Group Investigation of the Three-Dimensional Semi-Infinite Mixed Spin Ising Model. Zeitschrift für Physik B Condensed Matter, 81, 107-112. http://dx.doi.org/10.1007/BF01454221
Schofield, S.L. and Bowers, R.G. (1980) Renormalisation Group Calculations on a Mixed-Spin System in Two Dimensions. Journal of Physics A: Mathematical and General, 13, 3697. http://dx.doi.org/10.1088/0305-4470/13/12/019
Iwashia, T. and Uryu, N. (1983) The Effect of the Biquadratic Exchange Interaction on the Curie Temperature of the Mixed Ising Ferromagnet. Physics Letters A, 96, 311-313. http://dx.doi.org/10.1016/0375-9601(83)90187-1
Kaneyoshi, T. (1986) Role of Single-Ion Anisotropy in Amorphous Ferrimagnetic Alloys. Physical Review B, 34, 7866-7872. http://dx.doi.org/10.1103/PhysRevB.34.7866
Kaneyoshi, T. (1987) Curie Temperatures and Tricritical Points in Mixed Ising Ferromagnetic Systems. Journal of the Physical Society of Japan, 56, 2675-2680. http://dx.doi.org/10.1143/JPSJ.56.2675
Zhang, G.M. and Yang, C.Z. (1993) Monte Carlo Study of the Two-Dimensional Quadratic Ising Ferromagnet with Spins S = 1/2 and S = 1 and with Crystal-Field Interactions. Physical Review B, 48, 9452-9455. http://dx.doi.org/10.1103/PhysRevB.48.9452
Buendia, G.M. and Novotny, M.A. (1997) Numerical Study of a Mixed Ising Ferrimagnetic System. Journal of Physics: Condensed Matter, 9, 5951. http://dx.doi.org/10.1088/0953-8984/9/27/021
Benayad, N., Klumper, A., Zittartz, J. and Benyoussef, A. (1989) Re-Entrant Ferromagnetism in a Two-Dimensional Mixed Spin Ising Model with Random Nearest-Neighbour Interactions. Zeitschrift für Physik B Condensed Matter, 77, 333-338. http://dx.doi.org/10.1007/BF01313678
Bobák, A., Abubrig, O.F., Horváth, D. and Jascur, M. (2001) Mean-Field Solution of the Mixed Spin-1 and Spin- Full-Size Image ( http://dx.doi.org/10.1016/S0378-4371(01)00176-5
Albayrak, E. (2003) Mixed Spin-1 and Spin-3/2 Blume-Capel Ising Ferrimagnetic System on the Bethe Lattice. International Journal of Modern Physics B, 17, 1087. http://dx.doi.org/10.1142/S0217979203015978
Ekiz, C. (2006) The Possibility of Two Compensation Points in a Ferrimagnetic Mixed Spin-1 and Spin-3/2 Ising System Using Bethe Lattice Approach. Journal of Magnetism and Magnetic Materials, 307, 139-147. http://dx.doi.org/10.1016/j.jmmm.2006.03.059
Bobák, A. (1998) The Effect of Anisotropies on the Magnetic Properties of a Mixed Spin-1 and Spin-3/2 Ising Ferrimagnetic System. Physica A: Statistical Mechanics and Its Applications, 258, 140-156. http://dx.doi.org/10.1016/S0378-4371(98)00233-7
Bobák, A. (2000) Multicritical Points in the Mixed Spin-1 and Spin-3/2 Ising System on a Square Lattice with Different Single-Ion Anisotropies. Physica A: Statistical Mechanics and Its Applications, 286, 531-540. http://dx.doi.org/10.1016/S0378-4371(00)00404-0
Nakamura, Y. and Tucker, J.W. (2002) Monte Carlo Study of a Mixed Spin-1 and Spin-3/2 Ising Ferromagnet. IEEE Transactions on Magnetics, 38, 2406-2408. http://dx.doi.org/10.1109/TMAG.2002.803598
Mert, G. (2012) Green’s Function Study of a Mixed Spin-1 and Spin-3/2 Heisenberg Ferrimagnetic System. Journal of Magnetism and Magnetic Materials, 324, 2706-2710. http://dx.doi.org/10.1016/j.jmmm.2012.03.033
Yessoufou, R.A., Amoussa, S.H. and Hontinfinde, F. (2009) Magnetic Properties of the Mixed Spin-5/2 and Spin-3/2 Blume-Capel Ising System on the Two-Fold Cayley Tree. Central European Journal of Physics, 7, 555-567.
Madani, M., Gaye, A., El Bouziani, M. and Alrajhi, M. (2015) Migdal-Kadanoff Solution of the Mixed Spin-1 and Spin-3/2 Blume-Capel Model with Different Single-Ion Anisotropies. Physica A: Statistical Mechanics and Its Applications, 437, 396-404. http://dx.doi.org/10.1016/j.physa.2015.06.003
Migdal, A.A. (1975) Recursion Equations in Gauge Field Theories. Zh. Eksp. Teor. Fiz, 69, 810-822 [Soviet Physics—JETP, 42, (1975) 413-418].
Kadanoff, L.P. (2010) Notes on Migdal’s Recursion Formulas. Annals of Physics, 100, 359-394. http://dx.doi.org/10.1016/0003-4916(76)90066-X
Hasenbusch, M. (2010) Finite Size Scaling Study of Lattice Models in the Three-Dimensional Ising Universality Class. Physical Review B, 82, Article ID: 174433. http://dx.doi.org/10.1103/PhysRevB.82.174433
Abubrig, O.F., Horv1ath, D., Bobák, A. and Jascur, M. (2001) Mean-Field Solution of the Mixed Spin-1 and spin-3/2 Ising System with Different Single-Ion Anisotropies. Physica A: Statistical Mechanics and Its Applications, 296, 437-450. http://dx.doi.org/10.1016/S0378-4371(01)00176-5
Tucker, J.W. (2001) Mixed Spin 1-Spin 3/2 Blume-Capel Ising Ferromagnet. Journal of Magnetism and Magnetic Materials, 237, 215-224. http://dx.doi.org/10.1016/S0304-8853(01)00691-6
Niemeijer, Th. and van Leeuwen, J.M.J. (1976) Renormalization Theory for Ising-Like Spin Systems. In: Dom, C. and Green, M.S., Eds., Phase Transitions and Critical Phenomena, Vol. 6, Academic Press, New York, 425-505.
Lipowsky, R. and Wagner, H. (1981) The Migdal-Kadanoff Renormalization Group Scheme for the Ising Model with a Free Surface. Zeitschrift für Physik B Condensed Matter, 42, 355-365. http://dx.doi.org/10.1007/BF01293202
Nagai, O. and Toyonaga, M. (1981) Critical Behaviour of Ising Magnets: Infinitesimal Migdal-Kadanoff Approximation. Journal of Physics C: Solid State Physics, 14, L545.
Bakchich, A. and El Bouziani, M. (1997) Phase Diagrams of the Three-Dimensional Semi-Infinite Blume-Emery- Griffiths Model. Physical Review B, 56, 11155-11160. http://dx.doi.org/10.1103/PhysRevB.56.11155
Benyoussef, A., Boccara, N. and El Bouziani, M. (1986) Real-Space Renormalization-Group Investigation of the Three-Dimensional Semi-Infinite Blume-Emery-Griffiths Model. Physical Review B, 34, 7775-7783. http://dx.doi.org/10.1103/PhysRevB.34.7775
Bakchich, A. and El Bouziani, M. (1997) Surface Critical Behavior of the Semi-Infinite Blume-Emery-Griffiths Model. Physical Review B, 56, 11161-11168. http://dx.doi.org/10.1103/PhysRevB.56.11161
Lipowsky, R. (1982) The Semi-Infinite Potts Model: A New Low Temperature Phase. Zeitschrift für Physik B Condensed Matter, 45, 229-235.
Sundaram, V.S., Farrell, B., Alben, R.S. and Robertson, W.D. (1973) Order-Disorder Transformation at the {100} Surface of Cu 3 Au. Physical Review Letters, 31, 1136-1139. http://dx.doi.org/10.1103/PhysRevLett.31.1136
Lipowsky, R. (1983) Surface Induced Disordering at First-Order Bulk Transitions. Zeitschrift für Physik B Condensed Matter, 51, 165-172. http://dx.doi.org/10.1007/BF01308770