Dresden 2026 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 15: Focus Session: Large Deviations and Rare Events II
DY 15.5: Talk
Monday, March 9, 2026, 16:15–16:30, ZEU/0114
Universality of the order-parameter large-deviation function for the critical 2D Ising and Blume-Capel models — Nikolaos G. Fytas1, Víctor Martín-Mayor2, Attilio L. Stella3, Gianluca Teza4, Alexandros Vasilopoulos1, and •David Yllanes5 — 1University of Essex — 2Universidad Complutense de Madrid — 3Università di Padova — 4MPIPKS, Dresden — 5Universidad de Zaragoza
We revisit the longstanding question of universality in the probability density function (pdf) of the order parameter at criticality, traditionally assumed to hold only for the central region of the distribution. Focusing on the dimensionless magnetization u = m/√⟨ m2⟩, whose moments are universally defined in the thermodynamic limit, we hypothesize that universality extends to the full pdf pL(u), including its exponentially suppressed large-deviation tails scaling as u1+δ. We test this conjecture with large-scale Tethered Monte Carlo simulations of the 2D Blume-Capel model at criticality for several values of the crystal field Δ, including the Ising limit (Δ=−∞) and approaching the tricritical point Δc≈ 1.97. We simulate lattices up to L=4096 with a tethered cluster algorithm, reaching the asymptotic regime for probability densities as small as 10−200. Our results are strong numerical evidence for universality in the full pL(u) and settle the debated non-universality of the large-deviation function for m, where system-dependent amplitudes obscure scaling behavior. We consider the universality of the unusual combination of a finite-size amplitude with an amplitude for a scaling law related to the large-deviation function.
Keywords: Ising model; Blume Capel model; Universality; Large-deviation function; Tethered Monte Carlo