Critical probability distributions of the order parameter at two loops: II. O ( n ) universality class
Sankarshan Sahu · Journal of Statistical Mechanics Theory and Experiment · 2026
Abstract We show how to compute the probability distributions of the order parameter of the O ( n ) model at two-loop order of perturbation theory generalizing the methods developed for computing the same in case of the Ising model (Sahu 2025 J. Stat. Mech. 2025 123202). We show that even for the O ( n ) model, there exists not one but a family of these probability distribution functions (PDFs) indexed by ζ which is the ratio of system size L to the bulk correlation length ξ ∞ . We also compare these PDFs to the Monte-Carlo simulations and the existing FRG results (Rançon et al 2025 arXiv:2501.04465 [cond-mat.statmech]) for the O (2) and O (3) models.