PUB - Publikationen an der Universität Bielefeld

The critical behavior of the Ising model in the absence of an external magnetic field can be specified either through spontaneous symmetry breaking ( thermal criticality) or through cluster percolation ( geometric criticality). We extend this to finite external fields for the case of the Potts' model, showing that a geometric analysis leads to the same first-order/second-order structure as found in thermodynamic studies. We calculate the Kertesz line, separating percolating and non-percolating regimes, both analytically and numerically for the Potts model in the presence of an external magnetic field.