Two-dimensional spin models with macroscopic degeneracy

We consider a class of anisotropic spin-$\frac{1}{2}$ models with competing ferro- and antiferromagnetic interactions on two-dimensional Tasaki kagome lattices consisting corner sharing triangles. For certain values the ground state is macroscopically degenerated in zero magnetic field. In this case manifold consists isolated magnons as well bound magnon complexes. The degeneracy estimated using special form exact wave function which admits arrow configuration representation lattice. comparison estimate result for some exactly solved shows that used approach determines number states exponential accuracy. It shown main contribution to residual entropy given by