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Grassman path-integral solution for a class of triangular type decorated ising models

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  • Plechko, V.N.

Abstract

Grassman path-integral solution is given for a class of two-dimensional triangular type decorated Ising models. Canonical Ising Lattices, rectangular, triangular and hexagonal, enter into this class as the most simple particular cases. As a first step, the problem is reformulated in terms of a free-fermionic field theory. The method is based on the mirror-factorization principle for the density matrix; traditional transfer-matrix or combinatorial considerations are not needed. The solution exhibits the characteristics free-fermionic structure providing the universal logarithmic singularity in the specific heat. The symmetries and the critical-point behaviour are investigated within the spin-polynomial interpretation of the problem. Some concrete decorated lattices are treated by illustration. Attention is given to the choice of rational computational devices.

Suggested Citation

  • Plechko, V.N., 1988. "Grassman path-integral solution for a class of triangular type decorated ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(1), pages 51-97.
    • Handle: RePEc:eee:phsmap:v:152:y:1988:i:1:p:51-97
    DOI: 10.1016/0378-4371(88)90065-9
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    Cited by:

    1. Seke, J. & Soldatov, A.V. & Bogolubov, N.N., 1997. "The Seke self-consistent projection-operator approach for the calculation of quantum-mechanical eigenvalues and eigenstates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(1), pages 221-240.

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