A geometrical interpretation of critical exponents
Statistical Mechanics
2025-10-15 v2
Abstract
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function might be sensitive to this change in dimensionality. We discuss how this phenomenon is observable in growth processes and near critical points for systems in equilibrium. In particular, we determine the fractal dimension for the Ising model and validate it via computer simulations for two dimensions.
Keywords
Cite
@article{arxiv.2402.10167,
title = {A geometrical interpretation of critical exponents},
author = {Henrique A. Lima and Edwin E. Mozo Luis and Ismael S. S. Carrasco and Alex Hansen and Fernando A. Oliveira},
journal= {arXiv preprint arXiv:2402.10167},
year = {2025}
}