Abstract
The mixed spin Ising model (spins σ=1/2 andS=1) ond-dimensional hypercubic lattices with nearest-neighbour exchange interactions is studied via a renormalization group transformation in position space. The phase diagrams in (L, K) space, i.e. in dependence of the bilinear (K) and the biquadratic (L) interaction coefficients, are qualitatively different ford=2 andd>2. For any dimensiond however it is found that all transitions are of second order. At zero-temperature (K=∞,L=∞), the ferromagnetic order disappears at (L/K)0=2, which does not depend ond. Using an extension of this real-space renormalization group analysis we study the two-dimensional random disordered version of the above model.L is kept homogeneous and the bilinear interactionsK ij are assumed to be independent random variables with distributionP(K ij )=pδ(K ij −K)+(1−p)δ(K ij −αK); whereK>0. The phase diagrams for different values ofp are obtained. At zero temperature, it is found that in the bond diluted model (α=0) the value (L/K)0 depends continuously onp, whereas in the random ±K interactions (α=−1) (L/K)0 is unique and does not depend onp.
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References
Brown, H.A.: Phys. Rev. B4, 115 (1971)
Chen, H.H., Levy, P.M.: Phys. Rev. B7, 4284 (1973)
Siqueira, A.F., Fittipaldi, I.P.: Phys. Rev. B31, 6092 (1985)
Takahashi, K., Tanaka, M.: J. Phys. Soc Jpn46, 1428 (1979)
Berker, A.N., Wortis, M.: Phys. Rev. B14, 4948 (1976)
Benayad, N., Benyoussef, A., Boccara, N.: J. Phys. C18, 1899 (1985)
Dickinson, H., Yeomans, J.: J. Phys. C16, L345 (1983)
Schofield, S.L., Bowers, R.G.: J. Phys. A13, 3697 (1980)
Yousif, B.Y., Bowers, R.G.: J. Phys. A17, 3389 (1984)
Iwashita, T., Uryu, N.: Phys. Lett.96A, 311 (1979)
Iwashita, T., Uryu, N.: Phys. Soc. Jpn.53, 721 (1984)
Iwashita, T., Uryu, N.: Phys. Status Solidi (b)125, 551 (1981)
Kaneyoshi, T.: J. Phys. Soc. Jpn.56, 2675 (1987)
Benayad, N., Klümper, A., Zittartz, J., Benyoussef, A.: Z. Phys. B — Condensed Matter77, 339 (1989)
Migdal, A.A.: Zh. Eksp. Teor. Fiz.69, 1457 (1975) [Sov. Phys.-JETP42, 743 (1975)]
Kadanoff, L.P.: Ann. Phys. (N.Y.)100, 359 (1976)
Jayaprakash, C., Riedel, E.K., Wortis, M.: Phys. Rev. B18, 2244 (1978)
Yeomans, J.M., Stinchcombe, R.B.: J. Phys. C:12, 347 (1979)
Tsallis, C., Levy, S.V.F.: J. Phys. C:13, 465 (1980)
Benyoussef, A., Boccara, N.: J. Phys. C:15, 1381 (1982)
Nienhuis, B., Nauenberg, M.: Phys. Rev. Lett.35, 477 (1975)
Onsager, L.: Phys. Rev.65, 117 (1944)
Yang, C.N.: Phys. Rev.85, 809 (1952)
Sykes, M.F., Essam, J.W.: Phys. Rev.133A, 310 (1964)
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Supported by the agreement of cooperation between the DFGW. Germany and the CNR-Maroc
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Benayad, N. Real-space renormalization group investigation of pure and disordered mixed spin Ising models ond-dimensional lattices. Z. Physik B - Condensed Matter 81, 99–105 (1990). https://doi.org/10.1007/BF01454220
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DOI: https://doi.org/10.1007/BF01454220