Multicanonical simulation of the Domb-Joyce model and the Gō model: new enumeration methods for self-avoiding walks

24th IUPAP Conference on Computational Physics

物理学;计算机科学

Shirai, Nobu C.^1,2 ; Kikuchi, MacOto^1,2,3

Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan^1

Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan^2

Graduate School of Frontier Biosciences, Osaka University, Suita, Osaka 565-0871, Japan^3

关键词: Configuration space;    Enumeration method;    First-order phase transitions;    Generalized random walks;    Ground-state conformations;    Multicanonical Monte Carlo;    Multicanonical simulations;    Self avoiding walk;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/454/1/012039/pdf
DOI  :  10.1088/1742-6596/454/1/012039

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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 G 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 G 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 G model.