prof. dr hab. Adam Lipowski, UAM

Ising model on (un-⁠)directed random graphs

First, we recall some basic percolative properties of random undirected graphs and discuss the behaviour of the Ising model on such graphs. In particular, we emphasize that emergence of finite temperature ferromagnetism coincides with the percolation transition and a similar behaviour occours on some diluted cartesian lattices. Then, we examine Ising models on directed graphs. Such models do not obey the detailed balance but on some regular lattices they behave similarly to their equilibrium counterparts. Numerical simulations show that for directed random graphs to support finite temperature ferromagnetism the spanning cluster must be sufficiently dense. Similar behaviour appears in some other models with agreement dynamics.