Soluble kagome Ising model in a magnetic field

An Ising model on the kagome lattice with superexchange interactions is solved exactly under the presence of a nonzero external magnetic field. The model generalizes the superexchange model introduced by Fisher in 1960 and is analyzed in light of a free-fermion model. We deduce the critical condition and present detailed analyses of its thermodynamic and magnetic properties. The system is found to exhibit a second-order transition with logarithmic singularities at criticality.