Delta chain with ferromagnetic and antiferromagnetic interactions at the   critical point
  We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate with a large residual entropy per spin $s_0=\frac{1}{2}\ln 2$. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions. 
V.Ya. Krivnov, D.V. Dmitriev, S. Nishimoto, S.-L. Drechsler, J.   Richter
cond-mat.str-el