Antiferromagnetic Ising model with frustrations on Husimi lattice of polygons with odd number of sides

Antiferromagnetic Ising model on Husimi lattice of polygons with odd number of sides are exactly solved to investigate the frustration of spins. Recursive lattices of pentagon, heptagon and nonagon were studied. The spontaneous magnetizations of these systems can easily be located from the solution and entropy curve. The solutions present N branches from 0 to 1 below TC, and the asymmetric arrangement of solutions confirms the frustration, which also can be identified by the non-zero residual entropy at T = 0. As expected, the TC increases with the number of sides, while ST=0 decreases as a measure of the degree of frustration