The first order phase transitions in the multisite spin-1/2 model on a pure Husimi lattice

Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

“…Note that the existence of the single-point ground states was also shown in the framework of the antiferromagnetic spin-1/2 Ising model and the corresponding multisite model on the 'triangular' Husimi lattice, i.e. on the Husimi lattice constructed from elementary triangles with coordination number z = 6 [19,20]. However, all above mentioned models are spin-1/2 Ising and Ising-like models only and it is necessary to stress that, at the moment, there exists no exact solution of a higher spin value antiferromagnetic Ising model in the presence of external magnetic field on a well-defined geometrically frustrated lattice.…”

“…Note that solutions (20) with coecients (21)-( 23) have sense if and only if ≠ x 1 1 . Thus, to proceed we shall suppose that ≠…”

“…It is also important to realize that both solutions ( ) ± x 0 given in equation (20) are important in our analysis because, although always only one of them gives physically acceptable real positive solution of the system of equations ( 18) and (19), which of them is relevant in a concrete case depends in fact on the values of parameters K < 0 and ≠ h 0. Further, using the explicit expressions for ( )…”