Relaxation theory of spin-3/2 Ising system near phase transition temperatures

doi:10.1088/1674-1056/19/8/080516

摘要/Abstract

摘要： Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement.

Abstract: Dynamics of a spin-3/2 Ising system Hamiltonian with bilinear and biquadratic nearest-neighbour exchange interactions is studied by a simple method in which the statistical equilibrium theory is combined with the Onsager's theory of irreversible thermodynamics. First, the equilibrium behaviour of the model in the molecular-field approximation is given briefly in order to obtain the phase transition temperatures, i.e. the first- and second-order and the tricritical points. Then, the Onsager theory is applied to the model and the kinetic or rate equations are obtained. By solving these equations three relaxation times are calculated and their behaviours are examined for temperatures near the phase transition points. Moreover, the z dynamic critical exponent is calculated and compared with the z values obtained for different systems experimentally and theoretically, and they are found to be in good agrement.

Key words: spin-3/2 Ising system, Onsager theory

中图分类号: (Classical spin models)

75.10.Hk

75.10.Dg (Crystal-field theory and spin Hamiltonians) 75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.)) 75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)) 75.40.Gb (Dynamic properties?)

Osman Canko, Mustafa Keskin. Relaxation theory of spin-3/2 Ising system near phase transition temperatures[J]. 中国物理B, 2010, 19(8): 80516-080516.

Osman Canko and Mustafa Keskin. Relaxation theory of spin-3/2 Ising system near phase transition temperatures[J]. Chin. Phys. B, 2010, 19(8): 80516-080516.

参考文献 74

[1]	Sivardière J and Blume M 1972 Phys. Rev. B 5 1126
[2]	Krinsky S and Mukamel D 1975 Phys. Rev. B 11 399
[3]	Blume M, Emery V J and Griffiths R B 1971 Phys. Rev. A 4 1071
[4]	S'a Barreto F C and De Alcantara Bonfim O F 1991 Physica A 172 378
[5]	Tucker J W 2000 J. Magn. Magn. Mater. 214 121
[6]	Bakchich A and El Bouziani M 2001 J. Phys.: Condens. Matter 13 91
[7]	Albayrak E 2002 Phys. Rev. B 65 134429
[8]	Albayrak E and Keskin M 2002 J. Magn. Magn. Mater. 241 249, and references therein
[9]	Ekiz C, Albayrak E and Keskin M 2003 J. Magn. Magn. Mater. 256 311
[10]	Keskin M, Phinar M A, Erdincc A and Canko O 2006 Physica A 364 263
[11]	Canko O and Keskin M 2003 Phys. Lett. A 320 22
[12]	Blume M 1966 Phys. Rev. 141 517
[13]	Capel H W 1966 Physica (Utr) 32 966
[14]	Xavier J C, Alcaraz F C, Pen a Lara D and Plascak J A 1998 Phys. Rev. B 57 11 575
[15]	Plascak J A and Landau D P 2003 Phys. Rev. E 67 15103(R)
[16]	Grollau S 2002 Phys. Rev. E 65 56130, and references therein
[17]	Özsoy O, Albayrak E and Keskin M 2002 Physica A 304 443
[18]	Ekiz C 2004 J. Magn. Magn. Mater. 284 409
[19]	Grandi B C S and Figueiredo W 2004 Phys. Rev. E 70 056109
[20]	Keskin M, Canko O and Deviren B 2006 Phys. Rev. E 74 011110
[21]	Keskin M, Canko O and Khirak M 2007 J. Stat. Phys. 127 359
[22]	Canko O, Deviren B and Keskin M 2006 J. Phys.: Condens. Matter 18 6635
[23]	Keskin M, Deviren B, Canko O and Khirak M 2007 Acta Phys. Polonica B 38 2445
[24]	Keskin M, Canko O and Deviren B 2007 J. Magn. Magn. Mater. 313 L1
[25]	Canko O and Keskin M 2006 Physica A 363 315
[26]	Keskin M and Canko O 2008 J. Magn. Magn. Mater. 320 8
[27]	Keskin M and Canko O 2005 Phys. Lett. A 348 9
[28]	Onsager L 1931 Phys. Rev. 37 405
[29]	Onsager L 1931 Phys. Rev. 38 2265
[30]	Tanaka T, Meijer P H E and Barry J H 1962 J. Chem. Phys. 37 1397
[31]	Barry J H 1966 J. Chem. Phys. 45 4172
[32]	Barry J H and Harrington D A 1971 Phys. Rev. B 4 3068
[33]	Erdem R and Keskin M 2001 Phys. Stat. Sol. (b) 225 145
[34]	Erdem R and Keskin M 2001 Phys. Rev. E 64 026102
[35]	Keskin M and Erdem R 2002 Phys. Lett. A 297 427
[36]	Keskin M and Erdem R 2003 J. Chem. Phys. 118 5947
[37]	Erdem R and Keskin M 2001 Phys. Lett. A 291 159
[38]	Erdem R and Keskin M 2004 Phys. Lett. A 326 27
[39]	Erdem R and Keskin M 2003 Phys. Lett. A 310 74
[40]	Erdem R, Ekiz C and Keskin M 2003 Phys. Stat. Sol. (b) 240 220
[41]	Gulpinar G, Demirhan D and Buyukkilic F 2007 Phys. Rev. E 75 021104
[42]	Lei X W and Zheng B 2007 Phys. Rev. E 75 040104
[43]	Nogawa T and Nemoto K 2006 Phys. Rev. B 73 184504
[44]	Atsarkin V A, Demidov V V, Vasneva G A and Conder K 2001 Phys. Rev. B 63 092405
[45]	Etzkorn S J, Hibbs W, Miller J S and Epstein A J 2004 Phys. Rev. B 70 134419
[46]	Inoue H and Yonemitsu K 2007 Phys. Rev. B 75 235125
[47]	Kim E, Lee S J and Kim B 2007 Phys. Rev. E 75 021106
[48]	Bhowmik R N and Ranganathan R 2007 Phys. Rev. B 75 012410
[49]	Bonati C, Cannizzo A, Tonti D, Tortschanoff A, van Mourik F and Chergui M 2007 Phys. Rev. B 76 033304
[50]	Özsoy O and Keskin M 2003 Physica A 319 404
[51]	Canko O and Keskin M 2006 Int. J. Mod. Phys. B 20 455
[52]	Hohenberg P C and Halperin B I 1977 Rev. Mod. Phys. 49 435
[53]	Kawasaki K 1971 Phys. Rev. A 3 1097
[54]	Stanley H E 1971 Introduction to Phase Transitions and Critical Phenomena (New York: Oxford University Press)
[55]	Ray T S, Tamayo P and Klein W 1989 Phys. Rev. A 39 5949
[56]	Crisanti A and Ritort F 2003 J. Phys. A: Math. Gen. 36 R181
[57]	Pathria R K 1996 Statistical Mechanics (Oxford: Pergamon)
[58]	Belanger D P, Farago B, Jaccarino V, King A R, Lartigue C and Mezei F 1988 J. Phys. (Paris) Colloq. 49 C8-1229
[59]	Rosov N, Hohenemser C and Eibschütz M 1992 Phys. Rev. B 46 3452
[60]	Kohno H and Yao M 2002 J. Phys.: Condens. Matter 14 L171
[61]	Grassberger P 1995 Physica A 214 547 (Erratum 1995 217 227(E))
[62]	Ivaneyko D, Ilnytskyi J, Berche B and Holovatch Yu 2006 Physica A 370 163
[63]	Prudnikov V V, Ivanov A V and Fedorenko A A 1997 J. Exp. Theor. Phys. Lett. 66 835 (1997 Zh. Eksp. Teor. Fiz. 66 793)
[64]	Blavatśka V, Dudka M, Folk R and Holovatch Yu 2005 Phys. Rev. B 72 064417
[65]	Prudnikov V V and Vakilov A N 1992 J. Exp. Theor. Phys. Lett. 55 741 (1992 Zh. Eksp. Teor. Fiz. 55 709)
[66]	Wang F G and Hu C K 1997 Phys. Rev. E 56 2310
[67]	Wang J S 1992 Computer Simulation Studies in Condensed Matter Physics: XI ed. Landau D P, Mon K K and Schüttler H B (Heiderberg: Springer) p. 125
[68]	Murase Y 2007 Master Thesis, The University of Tokyo
[69]	Ozeki Y and Ito N 2007 J. Phys. A: Math. Theor. 40 R149
[70]	Miyashita S and Takano H 1985 Prog. Theor. Phys. 73 1122
[71]	Ito N 1993 Physica A 196 591
[72]	Nightingale M P and Blöte H W J 1996 Phys. Rev. Lett. 76 4548
[73]	Wang F G, Hatano N and Suziki M 1995 J. Phys. A 28 4543
[74]	Pleimling M and Igl'oi 2007 EPL 79 56002