1006.2208 (Chiaki Yamaguchi)

The Derivation of the Exact Internal Energies for Spin Glass Models by
Applying the Gauge Theory to the Fortuin-Kasteleyn Representation    [PDF]

Chiaki Yamaguchi

We derive the exact internal energies and the rigorous upper bounds of
specific heats for several spin glass models by applying the gauge theory to
the Fortuin-Kasteleyn representation which is a representation based on a
percolation picture for spin-spin correlation. The results are derived on the
Nishimori lines which are special lines on the phase diagrams. As the spin
glass models, the +-J Ising model and a Potts gauge glass model are studied.
The present solutions agree with the previous solutions. The derivation of the
solutions by the present method must be useful for understanding the
relationship between the percolation picture for spin-spin correlation and the
physical quantities on the Nishimori line.

View original: http://arxiv.org/abs/1006.2208