Self-consistency and Symmetry in d-dimensions

Details Self-consistency and Symmetry in d-dimensions Self-consistency and Symmetry in d-dimensions

1996-09-16

arxiv.org/abs/cond-mat/9609141v1

Phys. Rev. B 54 (1996) 15991-15996

Physics

Condensed Matter

16 pages, latex, Phys. Rev. B (in press)

Scientific paper

10.1103/PhysRevB.54.15991

Bethe approximation is shown to violate Bravais lattices translational invariance. A new scheme is then presented which goes over the one-site Weiss model yet preserving initial lattice symmetry. A mapping to a one-dimensional finite closed chain in an external field is obtained. Lattice topology determines the chain size. Using recent results in percolation, lattice connectivity between chains is argued to be $(q(d-1)-2)/(d)$ where $q$ is the coordination number and $d$ is the space dimension. A new self-consistent mean-field equation of state is derived. Critical temperatures are thus calculated for a large variety of lattices and dimensions. Results are within a few percent of exact estimates. Moreover onset of phase transitions is found to occur in the range $(d-1)q> 2$. For the Ising hypercube it yields the Golden number limit $d > (1+\sqrt 5)/(2)$.

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