Monotonicity theorems for integer-valued fields and delocalization in two-dimensionsQMAP Seminar
|Speaker:||Jacob Shapiro, Princeton University|
|Start time:||Fri, May 13 2022, 12:10PM|
Integer-valued fields are restricted to take values in Z and usually their Gibbs factor depends only on the gradient of the field. When the Gibbs factor is such that the typical value of the gradients is much larger than 1 (the spacing of points in Z), the integer constraint becomes less relevant so the field behaves as if it were real-valued and “delocalizes”. In 2D, this delocalization is associated with the Berezinskii–Kosterlitz–Thouless phase of the dual O(2) spin model. I will explain these notions for various models and present recent monotonicity theorems for fluctuations which are important to establish the delocalized phase.
Joint with: Michael Aizenman, Matan Harel and Ron Peled.