Fractal structure of Christ-Lee model
Statistical Mechanics
2025-03-28 v1 Pattern Formation and Solitons
Abstract
This paper numerically investigates the dynamical properties of kink and antikink collisions in the Christ_Lee model in the regime of epsilon approaching the phi4 theory. With given epsilon and the initial velocity Vin, we exhibiting the formation of bion, scattering, and n_bounce states. Additionally, we show the self_similar fractal structures in the plot of Vout_Vin with given epsilon. Specially, we find the fractal structure in the plot of Vout versus epsilon, which is not reported previously. We computes the Box_counting dimension for these fractal structures. We find that the Box_dimension is positively correlated with epsilon, and approaches to Hausdorff dimension of the Sierpinski triangle when epsilon is sufficiently large.
Keywords
Cite
@article{arxiv.2503.20799,
title = {Fractal structure of Christ-Lee model},
author = {Boming Zhang and Yunguo Jiang},
journal= {arXiv preprint arXiv:2503.20799},
year = {2025}
}