Journal of Statistical Mechanics: Theory and Experiment
Volume 2004
October 2004
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Iwan Jensen J. Stat. Mech. (2004) P10008 doi:10.1088/1742-5468/2004/10/P10008
Self-avoiding walks and polygons on the triangular lattice
Iwan Jensen
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| Figure 1. A snapshot of the boundary line (dashed line) during the transfer matrix calculation on the triangular lattice. SAWs are enumerated by successive moves of the kink in the boundary line so that one vertex (shaded) at a time is added to the rectangle. To the left of the boundary line we have drawn an example of a partially completed SAW. |
| Figure 2. The seven possible outputs from a single iteration of the TM algorithm. Depending on the states of the three vertices a, b, and d in the input, some of the outputs cannot occur. |
| Figure 3. Plots of estimates from third order differential approximants for 2 - α versus, respectively, the number of terms used by the differential approximants (left panel) and uc (right panel). |
| Figure 4. Plots of estimates from second order differential approximants for γ versus, respectively, the number of terms used by the differential approximants (left panel) and uc (right panel). |
| Figure 5. Estimates of the leading amplitude B plotted against 1/n using different numbers of terms in the asymptotic expansion (3.7). In the top panels we use the value μ = 4.150 797 226. The right panel just gives a more detailed look at the data shown in the left panel. In the bottom panels we use two different values μ = 4.150 797 20 (left panel) and μ = 4.150 797 25 (right panel) chosen to be at the extreme ends of our error-bounds for μ. |
| Figure 6. Estimates of the leading amplitude A for SAWs, AC/6 for the end-to-end distance, AD/6 for the radius of gyration, and AE/6 for the monomer distance from the end-points, plotted against 1/n using varying number of terms in the asymptotic expansion. |
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Self-avoiding walks and polygons on the triangular lattice
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