Spin-liquid behavior in the classical antiferromagnetic J1−J2−J3 spin system on the square-kagome lattice: Exact analysis within recursive-lattice approach

Magnetic and thermodynamic properties of the antiferromagnetic J1−J2−J3 spin system, i.e., the spin system with three different nearest-neighbor antiferromagnetic interactions, on the square-kagome lattice is investigated in the framework of the corresponding exactly solvable spin-1/2 Ising model on the recursive square-kagome lattice. The phase diagram of the model is found and it is shown that, depending on the model parameters, the model exhibits the existence of three long-range order (antiferromagnetic) phases, which are separated from the paramagnetic phase by the second order phase transitions. It is also shown that, in the zero temperature limit, the paramagnetic phase splits into three different ground states realized on the lines that separate antiferromagnetic ground states of the model. Due to the frustration, all these “paramagnetic” ground states are highly macroscopically degenerated with strict hierarchy of their residual entropies. Moreover, the high macroscopic degeneracy of the paramagnetic phase in the vicinity of these ground states together with the presence of strong correlations (given by the proximity of the second order phase transitions) allow one to consider the paramagnetic ground states as well as their immediate paramagnetic surroundings as regions with the classical spin-liquid behavior. It is also shown that the presence of the second order phase transitions in the vicinity of the paramagnetic ground states suppresses expected anomalous (Schottky-type) behavior of the specific heat related to the rapid entropy changes caused by the frustration.