Generalized tiling model models

D. Formulation of the Generalized Tiling Model for Two-Dimensional Melting... 

E. Statistical and Thermodynamic Properties of the Generalized Tiling Model... 

As we show below, the generalized tiling model we have developed exhibits very similar cooperative features that in general lead to a first-order transition. 

The properties of the generalized tiling model depend on two parameters, a dimensionless temperature t= kgTIE, and a dimensionless tiling fault energy r=EJE. We have obtained the statistical and thermodynamic properties of our model as a function of t and r from Metropolis Monte Carlo (MC) simulations. The basic variables used in the MC... 

We used Monte Carlo simulations to obtain the statistical and thermodynamic properties of topologically constrained and unconstrained versions of our model, for = 4 and = 6. For each of these versions of the generalized tiling model, we carried out heating runs (and a more... 

In Figs. 75 and 76 we have shown the order parameter internal energy per vertex (u = (H) /N) measured in MC simulations of the topologically constrained generalized tiling model for = 4, N = 3584. 

Figure 77. Internal energy versus t from Monte Carlo simulations of the topologically constrained generalized tiling model, for = 4, / = 28, N = 3584, obtained on heating (bullets) and cooling (circles).

Figure 84. Internal energy versus i from Monte Carlo simulations of the topologically unconstrained generalized tiling model, for =6, N = 896. Each series of simulations is labeled by its corresponding / -value, (a) Small r. (b) Large r.

In Tables IV-VIII we have compared the statistics of the topologically constrained and unconstrained generalized tiling models for r = 4, =... 

Figure 86. Small s part of n, calculated from relaxed configurations of the topologically constrained generalized tiling model for p = (>, r = 4, t = 1.4 (bullets). The solid line represents a fit to Eq. (3.26).

Figure 87. Relaxed configurations of the topologically unconstrained generalized tiling model for = r = 4, r = 0.635 (a) sweep 500 (b) sweep 1000 (c) sweep 1500 (d) sweep 2000 (e) sweep 5000 (/) sweep 12,000.

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