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Application of the transfer tensor method: A variational method

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  • Sobotta, G.

Abstract

We apply the transfer tensor method to get by a variational method approximated solutions of d-dimensional classical spin lattice models in statistical mechanics. We discuss the calculation of critical temperatures and also the limits, for which this variational method turns out to become exact. We apply this method to homogeneous and inhomogeneous Ising models. In the case of the 2-D random site model with nearest-neighbour interaction on a square lattice, the critical concentration xc is given by the solution of the equation x2(2x−x2+2) = 1 being xc=0.593905…, which seems to be consistent with the best known numerical result, xc≈0.593±0.002.

Suggested Citation

  • Sobotta, G., 1985. "Application of the transfer tensor method: A variational method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 457-471.
    • Handle: RePEc:eee:phsmap:v:132:y:1985:i:2:p:457-471
    DOI: 10.1016/0378-4371(85)90021-4
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