Abstract
This paper considers an averaging procedure for the description of a particles arrangement in a Hubbard model with antiferromagnetic interactions. The arrangements are described by the devil's staircase. Completeness of the staircase is proved.
Similar content being viewed by others
References
Bak, P. and Bruinsma, R.: One-dimensional Ising model and the complete devil's staircase, Phys. Rev. Lett. 49 (1982), 249–251.
Bernoulli, J., III.: Sur une nouvelle espèce de calcul, Recueil pour les astronomes (Berlin), Vol. 1, 1772, pp. 255–284.
Burkov, S. and Sinay, Ya.: Phase diagrams of one-dimensional lattice models with long-range antiferromagnetic interactions, Russian Math. Surveys 38(4) (1983), 235–257.
Delchamps, D.: Nonlinear dynamics of oversampling A-to-D converters, Proc. 32nd IEEE CDC, San-Antonio, 1993.
Feely, O. and Chua, L.: The effect of Integrator leak in Sigma-delta modulation, IEEE Trans. Circuits Systems 38 (1991), 1293–1305.
Gelig, A. and Churilov, A.: Stability and Oscillations in Nonlinear Pulse-modulated Systems, Birkhäuser, Basel, 1998.
Hardy, G. and Wright, E.: Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1976.
Hubbard, J.: Generalized Wigner lattices in one dimension and some applications to tetracianoquinodimethane (TCNQ) salts, Phys. Rev. B. 17 (1978), 494–505.
Jury, E.: Sampled-data Control Systems, Wiley, New York, 1958, 2nd edn, Krieger, 1977.
Kieffer, J. C.: Analysis of dc input response for a class of one-bit feedback encoders, IEEE Trans. Comm. 38(3) (1990), 337–340.
Kipnis, M. M.: Symbolic and chaotic dynamics of a pulse-width control system, Soviet Phys. Dokl. 324(2) (1992), 273–276.
Kipnis, M. M.: On the formalizations of the even 2-colouring, Proc. Chelyabinsk Pedagogical Univ. Series 4. Natural Sciences 1 (1996), 96–104.
Kipnis, M. M.: One-dimensional model of statistical mechanics with the Hubbard Hamiltonian and the interaction function, free from the convexity condition, Phys. Dokl. 336(3) (1994), 316–319.
Kipnis, M. M.: Boolean Averaging in a statistical mechanics model and in an analog-to-digital converter, Russian J. Math. Phys. 14(3) (1996), 397–402.
Leonov, N. N.: On the pointwise transformation of the line in itself, Izv. Vyssh. Uchebn. Zaved. Radiofiz. 2(6) (1959), 942–956 (in Russian).
Markoff, A.: Sur une question de Jean Bernoulli, Mat. Ann. 19 (1882), 27–36.
Morse, M. and Hedlund, G.: Symbolic dynamics II: Sturmian trajectories, Amer. J. Math. 62 (1940), 1–42.
Park, S. and Gray, R.: Sigma-delta modulation with leaky integration and constant input, IEEE Trans. Inf. Theory 38 (1992), 1512–1533.
Rockmore, D., Siegel, R., Tongring, N. and Tresser, C.: An approach to renormalization on n-torus, Chaos 1(1) (1991), 25–30.
Siegel, R., Tresser, C. and Zettler, G.: A decoding problem in dynamics and in number theory, Chaos 2(4) (1992), 473–493.
Smith, H. J. S.: Note on continued fraction, Messenger Math. VI (1877), 1–14.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kipnis, M.M. Periodic Ground State Configurations in a One-Dimensional Hubbard Model of Statistical Mechanics. Mathematical Physics, Analysis and Geometry 3, 101–115 (2000). https://doi.org/10.1023/A:1009822530189
Issue Date:
DOI: https://doi.org/10.1023/A:1009822530189