Leírás
Abstract: The most known example of an order-disorder phase transition is the Ising model that describes dependence of magnetic properties on the temperature T. This model on assignments of +1 and -1 to the sites is defined by nearest-neighbour interactions which get weaker when T increases - the correlations are uniformly positive below T_c and decay polynomially in the distance above T_c.
The loop O(n) model introduced in Physics in 1980 can be viewed as a generalisation of the Ising model where long-range interactions are added - the probability depends on the number of connected components of +1 and -1. Up to some extent, the loop O(n) model can be compared to the Fortuin-Kasteleyn (FK) percolation, though the set of parameters where it is conjectured to be conformally invariant is significantly wider.
In this talk, we will discuss recent results and open problems concerning the phase diagrams of the loop O(n) and the FK models.