Glass Transition in a Binary Mixture

There are two kinds of fix point solutions of the RR that describe the bulk behavior [15]. In the 1-cycle solution, the fix point solution becomes independent of the index m as we move toward the origin m = 0 on an infinite cactus, and is represented by x. For the current problem, it is given by x = 1 /2, as can be checked explicitly by the above RR in (10.48). It is obvious that it exists at all temperatures. There is no singularity in this fix point solution at any temperature. This solution corresponds to the disordered paramagnetic phase at high temperatures and the SMS below the melting transition to be discussed below. The other fix point solution is a 2-cycle solution, which has been found and discussed earlier in the semiflexible polymer problem [36, 37, 44, 46-48], the dimer model ]37], and the star and dendrimer solutions [48]. The fix point solution alternates between two values xj and x on two successive levels. At T = 0, this solution is given either by xj = 1 and x = 0, or by Xj = 0 and xj = 1. The system picks one of these as the solution. At and near T = 0, this solution corresponds to the low-temperature AF ordered phase, which represents the CR and its excitation at equal occupation, and can be obtained numerically. The 

1- cycle free energy is calculated by the general method proposed in Ref. [15], and the 

We now discuss numerical results. We take / = 0.01. The ground-state energy 

At T = 0, (T) — d-3466, while the CR entropy is zero, as expected. Thus, both 

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