Multicanonical simulation of the Domb-Joyce model and the Go model: new enumeration methods for self-avoiding walks
| Autor: | Shirai, Nobu C., Kikuchi, Macoto |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | J. Phys.: Conf. Ser. 454 012039 (2013) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/454/1/012039 |
| Popis: | We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding walks up to N=256 with statistical errors. The developed methods are based on statistical mechanical models of paths which include self-avoiding walks. The criterion for selecting a suitable model for enumerating self-avoiding walks is whether or not the configuration space of the model includes a set for which the number of the elements can be exactly counted. We call this set a scale fixing set. We selected the following two models which satisfy the criterion: the Go model for lattice proteins and the Domb-Joyce model for generalized random walks. There is a contrast between these two models in the structures of the configuration space. The configuration space of the Go model is defined as the universal set of self-avoiding walks, and the set of the ground state conformation provides a scale fixing set. On the other hand, the configuration space of the Domb-Joyce model is defined as the universal set of random walks which can be used as a scale fixing set, and the set of the ground state conformation is the same as the universal set of self-avoiding walks. From the perspective of enumeration performance, we conclude that the Domb-Joyce model is the better of the two. The reason for the performance difference is partly explained by the existence of the first-order phase transition of the Go model. Comment: 10 pages, 8 figures, 1 table, 1 algorithm. To appear in the proceedings of the Conference on Computational Physics, 2012 |
| Databáze: | arXiv |
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