Abstract
Lattice models such as Ising or Potts models are very often successfully applied to order-disorder phenomena in solids (e.g., for alloys) or on surfaces (e.g., for physisorption). In this contribution it is shown how to derive such models from a microscopic Hamiltonian in the framework of classical statistical mechanics. Both structural relaxations and thermal fluctuations can be incorporated within the (temperature-dependent) parameters of the lattice model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. G. Caflisch, A. N. Berker, and M. Kardar, Reentrant melting of krypton adsorbed on graphite and the helical Potts lattice-gas model,Phys. Rev. B 31:4527–4537 (1979).
S. Ostlund and A. N. Berker, Multicritical phase diagram of gases adsorbed on graphite: Temperature variation and finite-size effects.Phys. Rev. Lett. 42:843–846 (1985).
Z. W. Lu, S.-H. Wei, A. Zunger, S. Frota-Pessoa, and L. G. Ferreira, First-principles statistical mechanics of structural stability of intermetallic compounds,Phys. Rev. B 44:512–544 (1991).
I. I. Mazin, A. I. Liechtenstein, O. Gunnarson, O. K. Andersen, and V. P. Antropov, Orientational order in A3C60: Antiferromagnetic Ising model for the fcc lattice.Phys. Rev. Lett. 70:4142–4145 (1993).
J. D. Murray,Asymptotic Analysis (Springer-Verlag, 1984).
L. Sirovich,Techniques of Asymptotic Analysis (Springer-Verlag, 1971).
D. J. Bergman and B. I. Halperin, Critical behavior of an Ising model on a cubic compressible lattice,Phys. Rev. B 13:2145–2175 (1976).
H. Wagner and J. Swift, Elasticity of a magnetic lattice near the magnetic critical point,Z. Phys. 239:182–196 (1970).
J. M. Sanchez, F. Ducastelle, and D. Gratias, Generalized cluster description of multicomponent systems,Physica 128A:334–350 (1984).
R. Magri, S.-H. Wei, and A. Zunger, Ground-state structures and the random-state energy of the Madelung lattice,Phys. Rev. B 42:11388–11391 (1990).
A. Chiolero, unpublished.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chiolero, A., Baeriswyl, D. Structural relaxations, phonons, and Ising models. J Stat Phys 76, 347–360 (1994). https://doi.org/10.1007/BF02188666
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02188666