On the Kertész line: Thermodynamic versus Geometric Criticality

Details On the Kertész line: Thermodynamic versus Geometric Criticality On the Kertész line: Thermodynamic versus Geometric Criticality

2007-11-07

arxiv.org/abs/0711.1148v2

Journal of Physics A Mathematical and Theoretical 41, 8 (2008) 085001

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1751-8113/41/8/085001

The critical behaviour 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 Kert\'esz line, separating percolating and non-percolating regimes, both analytically and numerically for the Potts model in presence of an external magnetic field.

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