Configurations of 8-vertex model are orientations of edges of Z2 such that, around each vertex of Z2 , there are 0, 2 or 4 incoming edges. Hence, around each vertex of Z2 , there exists 8 available local configurations of orientations of its 4 adjacent edges. At each of these 8 local configurations, we associate a weight and, from these local weights, we define a law P of type Boltzmann on the set of configurations of 8-vertex models.
In this talk, we are interested by the joint law of orientations of two distant edges in Z2 oriented according to P , i.e. the edge correlation function. Under some conditions on local weights (integrability conditions as physicists say), we find a closed form for this function. This is due to the fact that, under these conditions on local weights, 8-vertex model has links with a probabilistic cellular automaton of order 2 and, also, with a system of particles in interaction.
Biography
Jérôme Casse is a postdoc at NYU Shanghai. He obtained his Ph.D. at University of Bordeaux, supervised by Jean-François Marckert. He was also a research and teaching assistant at Mines Nancy and in the probability group of IECL, University of Lorraine. His research interests include probabilistic cellular automata and their applications in combinatorics and statistical physics and, also, the iterated Brownian motion ad libitum.