Critical Probability Distributions of the order parameter at two loops II: $O(n)$ universality class

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 \cite{Sahu:2025bkp}. We show that even for the $O(n)$ model, there exists not one but a family of these probability distribution functions indexed by $\zeta$ which is the ratio of system size $L$ to the bulk correlation length ${\xi }_{\infty }$. We also compare these PDFs to the Monte-Carlo simulations and the existing FRG results for the $O(2)$ and $O(3)$ models.

13 pages (including the appendix), 7 figures

References in corpus (3)

• Anomalous dynamical scaling determines universal critical singularities
• Generalization of the Central Limit Theorem to Critical Systems: Revisiting Perturbation Theory
• Critical Probability Distributions of the order parameter at two loops I: Ising universality class

Cited by in corpus (1)

• Constraint effective action and critical correlation functions at fixed magnetization