Kagome-like chains with anisotropic ferromagnetic and antiferromagnetic interactions

We consider a spin-$\frac{1}{2}$ kagome-like chain with competing ferro- and antiferromagnetic anisotropic exchange interactions. The ground state phase diagram of this model consists of the ferromagnetic and ferrimagnetic phases. We study the ground state and the low-temperature properties on the phase boundary between these phases. The ground state on this phase boundary is macroscopically degenerate and consists of localized magnon states. We calculate the ground state degeneracy and corresponding residual entropy. The spontaneous magnetization has a jump on the phase boundary confirming the first-order type of the phase transition. In the limit of a strong anisotropy the spectrum of the low-energy excitations has multi-scale structure governing the peculiar features of the specific heat behavior.