On Continuous-Time Self-Avoiding Random Walk in Dimension Four |
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Authors: | Suemi Rodríguez-Romo Vladimir Tchijov |
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Institution: | (1) Centre of Theoretical Research, UNAM, Campus Cuautitlán, Apdo, Postal 95, Unidad Militar, Cuautitlán Izcalli, Estado de México, 54768, México; |
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Abstract: | We study the distribution of the end-to-end distance of continuous-time self-avoiding random walks (CTRW) in dimension four from two viewpoints. From a real-space renormalization-group map on probabilities, we conjecture the asymptotic behavior of the end-to-end distance of a weakly self-avoiding random walk (SARW) that penalizes two-body interactions of random walks in dimension four on a hierarchical lattice. Then we perform the Monte Carlo computer simulations of CTRW on the four-dimensional integer lattice, paying special attention to the difference in statistical behavior of the CTRW compared with the discrete-time random walks. In this framework, we verify the result already predicted by the renormalization-group method and provide new results related to enumeration of self-avoiding random walks and calculation of the mean square end-to-end distance and gyration radius of continous-time self-avoiding random walks. |
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Keywords: | Continuous-time self-avoiding random walk renormalization-group map dimerization algorithm Monte Carlo simulation |
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