J${\displaystyle {}_1}$-J${\displaystyle {}_2}$-J${\displaystyle {}_3}$ Model with Long-Range Lieb-Mattis Interaction

Stimulated by the two-dimensional frustrated Heisenberg antiferromagnet with first-, second-, and third-neighbor couplings (J${\displaystyle {}_1}$-J${\displaystyle {}_2}$-J${\displaystyle {}_3}$ model) we consider a corresponding three-parameter model with a long-range antiferromagnetic Lieb-Mattis interaction. This model can be solved exactly and leads to a better understanding of the role of frustration in the J${\displaystyle {}_1}$-J${\displaystyle {}_2}$-J${\displaystyle {}_3}$ model. We calculate the correlations in the groundstate and consider their finite size behavior. Furthermore we present the full thermodynamic phase diagram. We find the possibility of a disordered phase at T=0.