Abstract
We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.
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References
J. L. Monroe,J. Stat. Phys. 65:255 (1991).
B. Widom,J. Chem. Phys. 88:6508 (1984).
H. L. Scott,Phys. Rev. A 37:263 (1988).
X. N. Wu and F. Y. Wu,J. Phys. A: Math. Gen. 22:L1031 (1989).
R. J. Baxter and F. Y. Wu,Phys. Rev. Lett. 31:1294 (1973);Aust. J. Phys. 27:357 (1974).
S. Froyen, Aa. S. Svdbo, and P. C. Hemmer,Physica 85A:399 (1976).
J. Doczi-Reger and P. C. Hemmer,Physica 109A:541 (1981).
M. Schick, J. S. Walker, and M. Wortis,Phys. Rev. B 16:2205 (1977).
A. Malakis,J. Stat. Phys. 27:1 (1982).
K. K. Chin and D. P. Landau,Phys. Rev. B 36:275 (1987).
F. Y. Wu, Private communication.
C. J. Thompson,J. Stat. Phys. 27:441 (1982).
J. Slawny, inPhase Transition and Critical Phenomena, Vol. 11, C. Domb and J. J. Lebowitz, eds. (Academic Press, 1986).
T. P. Eggarter,Phys. Rev. 89:2989 (1974).
J. VonHeimburg and H. Thomas,J. Phys. C 7:3433 (1974).
E. Muller-Hartman and J. Zittartz,Phys. Rev. Lett. 33:893 (1974).
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, 1982), Chapter 4.
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Monroe, J.L. Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems. J Stat Phys 67, 1185–1200 (1992). https://doi.org/10.1007/BF01049014
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DOI: https://doi.org/10.1007/BF01049014