On a soluble model of an antiferromagnetic chain with alternating interactions and magnetic moments

The one-dimensional anisotropic XY model with alternating nearest-neighbour interactions and magnetic moments is investigated. The singularities of the susceptibility χzz in the ground state are studied in detail. In the general anisotropic case χzz can exhibit two logarithmic singularities at two different values of the applied magnetic field b. If the interactions satisfy a certain relation which will be reffered to as the pseudoisotropic condition (which includes the isotropic case), χzz can have two power-12 singularities at the upper side of the lower critical field and the lower side of the upper critical field. Deviations from this behaviour which occur for special values of the interaction constants are discussed in some detail. Finally the specific heat is studied in the low- and high-temperature limits.