5 Nov 2026, 16:30 h, room -1.08 

Lucas D'Alimonte (Institut Camille Jordan, Lyon)

Abstract: The lattice Ising model is one of the most studied spin models in the field of rigorous statistical mechanics. It was introduced in 1920 by Lenz, and ever since has been the cornerstone of many amazing developments in mathematical physics. One of its main features is the existence of a phase transition in the model: when the temperature drops below a certain threshold, the symmetry of the spin space can be spontaneously broken by the presence of suitable boundary conditions. A mesmerizing prediction, due to Paul Ehrenfest, is that the temperature at which the phase transition occurs should be the only real parameter at which certain thermodynamic quantities of the model fail to be analytic, when seen as functions of the complex temperature. In this talk I will present some recent results validating this correspondance: after constructing natural complex extensions of local observables of the Ising model, we will show that the spontaneous magnetisation of the model is indeed analytic away from the critical point, in any dimension. This is joint work with Loïc Gassmann (University of Fribourg).