Abstract.
Hamiltonians for general multi-state spin-glass systems with Ising symmetry are derived for both sequential and synchronous updating of the spins. The possibly different behaviour caused by the way of updating is studied in detail for the (anti)-ferromagnetic version of the models, which can be solved analytically without any approximation, both thermodynamically via a free-energy calculation and dynamically using the generating functional approach. Phase diagrams are discussed and the appearance of two-cycles in the case of synchronous updating is examined. A comparative study is made for the Q-Ising and the Blume-Emery-Griffiths ferromagnets and some interesting physical differences are found. Numerical simulations confirm the results obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Pérez Castillo, N.S. Skantzos, J. Phys. A 37, 9087 (2004)
N.S. Skantzos, A.C.C. Coolen, J. Phys. A 33, 1841 (2000)
P. Peretto, Biol. Cybern. 50, 51 (1984)
N.S. Skantzos, A.C.C. Coolen, J. Phys. A 33, 5785 (2000)
J.F. Fontanari, R. Köberle, J. Phys. France 49, 13 (1988)
D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1972)
H. Nishimori, 1997 TITECH technical report, unpublished
H. Rieger, J. Phys. A 23, L1273 (1990)
S.K. Ghatak, D. Sherrington, J. Phys. C 10, 3149 (1977)
W.A. Little, Math. Biosci. 19, 101 (1974)
W.A. Little, G.L. Shaw, Math. Biosci. 39, 281 (1978)
H.W. Capel, Physica 32, 966 (1966); M. Blume, Phys. Rev. 141, 517 (1966); M. Blume, V.J. Emery, R.B. Griffiths, Phys. Rev. A 4, 1071 (1971)
J.M. de Araújo, F.A. da Costa, F.D. Nobre, Eur. Phys. J. B 14, 661 (2000)
A. Crisanti, L. Leuzzi, Phys. Rev. B 70, 014409 (2004)
D.R.C. Dominguez, E. Korutcheva, Phys. Rev. E 62, 2620 (2000)
D. Bollé, T. Verbeiren, Phys. Lett. A 297, 156 (2002)
D. Bollé, in Advances in condensed matter and statistical mechanics, edited by E. Korutcheva, R. Cuerno (Nova Science Publishers, New York, 2004), p. 319
A.C.C Coolen, in Handbook of Biological Physics, Vol. 4 edited by F. Moss, S. Gielen (Elsevier Science B.V., 2001), p. 531
P.C. Martin, E.D. Siggia, H.A. Rose, Phys. Rev. A 8, 423 (1973)
A.C.C Coolen, in Handbook of Biological Physics, Vol. 4 edited by F. Moss, S. Gielen (Elsevier Science B.V., 2001), p. 597
D. Bedeaux, K. Lakatos-Lindenberg, K. Shuler, J. Math. Phys. 12, 2116 (1971)
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 9 August 2004,
PACS:
05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models
Rights and permissions
About this article
Cite this article
Bollé, D., Busquets Blanco, J. Two-cycles in spin-systems: sequential versus synchronous updating in multi-state Ising-type ferromagnets. Eur. Phys. J. B 42, 397–406 (2004). https://doi.org/10.1140/epjb/e2004-00396-1
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2004-00396-1