Universal and non-universal large deviations in critical systems

Abstract

Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics and challenge existing assumptions about power-law corrections to the leading stretched exponential decay in these tails.

v1) 17 pages, 8 figures; v2) minor corrections, published version

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Cited by in corpus (4)

• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Constraint effective action and critical correlation functions at fixed magnetization
• Constraint correlation functions of the one-dimensional Ising model in the scaling limit
• Observation of universal non-Gaussian statistics of the order parameter across a continuous phase transition