- 98-612 Chayes L., Coniglio A., Machta J., Shtengel K.
- The Mean Field Theory for
Percolation Models of the Ising Type
Sep 19, 98
(auto. generated ps),
of related papers
Abstract. The $q=2$ random cluster model is studied in the context of two mean--field
The Bethe lattice and the complete graph. For these systems, the critical
are defined in terms of finite clusters have some anomalous values as the
is approached from the high--density side which vindicates the results of
studies. In particular, the exponent $\tilde \gamma^\prime$ which
divergence of the average size of finite clusters is 1/2 and
$\tilde\nu^\prime$, the exponent associated with the length scale of finite
1/4. The full collection of exponents indicates an upper critical
dimension of 6.
The standard mean--field exponents of the Ising system are also present in
this model ($\nu^\prime = 1/2$, $\gamma^\prime = 1$) which implies, in
presence of two diverging length--scales. Furthermore, the
finite cluster exponents are stable to the addition of disorder which, near
critical dimension, may have interesting implications concerning the
generality of the
disordered system/correlation length bounds.