Finite-field phase transitions and criticality in a generalized kagomé Ising ferromagnet: Exact solutions

The standard two-parameter (nearest-neighbor pair-interaction J2 and magnetic field h) planar Ising model ferromagnet only has phase transitions in zero field. We generalize a standard kagomé Ising model ferromagnet by adding localized triplet Ising interactions J3. Exact solutions are obtained for the phase diagrams of the three-parameter model, demonstrating finite-field phase transitions and criticality. Necessary conditions for the latter findings include the pair-interaction parameter being ferromagnetic (J2>0), the applied field parameter competing against the intrinsic triplet-interaction parameter, the ratio of the triplet- and pair-interaction parameters residing within a determined finite symmetrical interval, and the field parameter being properly tuned, viz., tracing the pertinent field vs temperature phase boundary curve. The curvilinear shape of the phase boundary facilitates the relative strength |J3|∕J2 of the triplet interaction to be experimentally accessible. Employing generalized fluid–magnet correspondence relations, it is mathematically convenient and informative to affiliate the above magnetic phase diagrams with the corresponding fluid phase diagrams of the associated generalized kagomé lattice-gas model.