Title: Critical Probability Distributions of the Order Parameter: A new testing ground for Universality.
Abstract: Characterizing universality classes by means of their two leading independent critical exponents can be problematic, as these exponents are often difficult to determine accurately, both numerically and experimentally. I will argue that a more robust characterization can be achieved by focusing on universal functions rather than universal numbers, and in particular on the probability distribution function (PDF) of the order parameter. I will show that, due to the existence of non-commuting limits, there are in fact infinitely many such universal PDFs at criticality. I will outline how these distributions can be computed using perturbative functional renormalization group methods both at one-loop and two-loop orders . As a by-product, this framework provides a natural generalization of the Central Limit Theorem to strongly correlated random variables. For the three-dimensional Ising and $O(n)$ models, I will show that the agreement between numerical simulations and two-loop calculations is excellent. I will conclude by briefly discussing possible extensions of this approach to systems out of thermal equilibrium, as well as to gauge theories.
Note: This seminar will be happening in-person only.
Location: Huxley 145, 15.00-16.00.