On the Kertész line: Thermodynamic versus Geometric Criticality

Abstract

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 Kertész line, separating percolating and non-percolating regimes, both analytically and numerically for the Potts model in presence of an external magnetic field.

References in corpus (2)

• The three-dimensional, three-state Potts Model in an External Field
• Rigorous Analysis of Singularities and Absence of Analytic Continuation at First Order Phase Transition Points in Lattice Spin Models

Cited by in corpus (7)

• The Phase Diagram of Hadronic Matter
• A note on exponential decay in the random field Ising model
• The nature of symmetry breaking in the superconducting ground state
• A reanalysis of Finite Temperature SU(N) Gauge Theory
• Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line
• On the Kertész line: Some rigorous bounds
• Statistics of geometric clusters in Potts model: statistical mechanics approach