Facilitated Ising model

Adam-Gibbs relationship between them holds. 

60 the Fredrickson-Andersen facilitated Ising model on a square lattice. The line was calcu- 

1 50 rameters fixed by the linear relaxation behavior of the model. (From Fredrickson 1986, 

45 with permission Irom the Annual Review of Physical Chemistry, Volume 39, 1988, by 

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Figure 4.26 The log of the average relaxation time versus Adam-Gibbs exponent U jlTS for the facilitated Ising model on the square lattice. The points are from Monte Carlo simulations and the straight line through the points is the prediction of the Adam-Gibbs theory. (From Fredrickson 1988, with permission from the Annual Review of Physical Chemistry, Volume 39, 1988, by Annual Reviews, Inc.)...

This variant of random-site percolation considers the more general case in which the particles, instead of being randomly distributed, are correlated due to interactions between them. The most studied case is percolation in the lattice gas (Ising model) where the particles interact via an attractive nearest-neighbor force and are distributed in thermal equilibrium For any temperature T there is a density percolation threshold Pc(T), (Since in this model p is the density of occupied sites and not the probability of bond formation, it is of no direct relevance to gelation but represents an intermediate step in the more complicated model which is discussed in Chapter D.) In the limit T (or zero interaction) the particles are distributed randomly, and pc( ) is thus the random-site percolation threshold. When T decreases, attractive interactions facilitate the formation of clusters therefore, Pc(T) decreases with falling T while the clusters become more compacP ... 

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