# Malin Palö Forsström: Color representations of Ising models

**Time: **
Wed 2020-03-11 15.15 - 16.15

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

**Lecturer: **
Malin Palö Forsström, KTH

### Abstract

In a paper by J. Steif and J. Tykesson from 2017, the authors defined the so-called general divide and color model. One of the most well-known examples of such a model is the Ising model with no external field, which has a color representation given by the random cluster model. In this talk, we give necessary and sufficient conditions for this representation being unique. We also show that if one considers the Ising model on a complete graph, then for many h > 0, there is no color representation. This shows in particular that generalizations of the random cluster model of Ising models to positive external fields cannot, in general, be a color representation. Finally, we discuss the properties of the color representations of Ising models when the external fields tend to zero.