Chimeric critical phenomena of non-local cascades at mixed-order phase transitionsOnline: attend (945856)

In systems with positive feedback, microscopic changes cause macroscopic effects, cascading up to length scales determined by the feedback range. Long-range feedback, in particular, generate cascades that can propagate at all distances resulting in abrupt transitions with critical scaling. These intriguing transitions, often called hybrid or mixed-order [1, 2], have been reported somewhere theoretically, somewhere numerically on both random and spatial graphs, typically in ad hoc models. In this talk, we will show that their critical phenomena can be cast in a coherent statistical mechanics framework, predicting two universality classes of mixed-order transitions by long-range cascades defined by the parity invariance of the underlying process [3]. We will provide finite-size scaling arguments based on hyperscaling above upper critical dimensions [4], predicting critical exponents having both mean-field and $d$-dimensional features –hence, their term "chimeric''– for any $d\geq2$ and show how parity invariance influences the geometry and lifetime of avalanches. We will demonstrate the validity of such framework in several synthetic and experimentally-driven cascade models, with a particular emphasis on interdependent processes [5, 6], given their recent observation in laboratory experiments [7].

[1] R. M. D’Souza, J. Gómez-Gardenes, J. Nagler, and A. Arena, Advances in Physics, 68(3):123–223, 2019. [2] C. Kuehn and C. Bick, Science advances, 7(16):eabe3824, 2021. [3] I. B., B. Gross, J.Kertész, S. Havlin, arXiv preprint arXiv:2401.09313, 2024. [4] B. Berche, T. Ellis, Y. Holovatch, and R. Kenna, SciPost Physics Lecture Notes, 060, 2022. [5] S. V. Buldyrev et al., Nature 464.7291, 1025-1028, 2010. [6] M. M. Danziger, I. B., S. Boccaletti, S. Havlin, Nature Physics, 15(2), 178-185, 2019. [7] I.B. et al.,Nature Physics 19, 1163–1170 (2023).