20. Apr 2026

One-arm exponents for the high dimensional Ising model

Vienna Probability Seminar

Datum: 20. April 2026 | 17:00 – 18:00
Sprecher: Diederik van Engelenburg, TU Wien
Veranstaltungsort: Central Bldg / O1 / Mondi 2a (I01.O1.008)
Sprache: Englisch

In this talk, I will focus on behavior of the Ising model in high dimensions (d 4). Widom proposed that thermodynamic quantities follow power laws governed by critical exponents, and above the upper critical dimension d_c = 4, these exponents reduce to the mean-field values (matching those on trees or complete graphs). I will talk about a recent work about the so-called one-arm event (the origin connects to distance n) in the FK-Ising model. We observe that this exponent depends on the boundary condition: for wired boundary conditions, we prove that this probability decays up to constants as n^(-1) for d 4, whereas in infinite volume we prove that it decays as n^(-2) for d 6, but not for d = 4, 5.