Colloquium Mathematics: Eric Endo (PhD student/Bernoulli Institute RUG)
|When:||Th 28-06-2018 16:00 - 17:00|
|Where:||5161.0105 (Bernoulliborg), Nijenborgh 9, Groningen|
Title: G-measures and external fields for long-range Ising models
Long-range Ising models are one-dimensional Ising models with long-range interactions that decay polynomially. There are several results to show for which powers of the interaction decay the phase transition occurs at low temperature, and results that describe the phase-separating point.
g-measures are a generalisation of Markov chains that include past dependence of infinite length, consistent to a continuous function called g-function.
Here, we present the result that, using results on the phase-separating point, the Gibbs measures of the long range Ising model display a wetting transition at sufficiently low temperature, concluding that these measures are not g-measures since there us a lack of the continuity of the candidate g-function. We also present the existence of a phase transition at low temperature when the model is in the presence of a positive external field decaying to zero fast enough.