Spin correlation functions of some frustrated ultra-small classical Heisenberg clusters

We obtain analytical expressions for the spin correlation functions and zero-field susceptibility of small clusters of classical Heisenberg spins. The clusters consist of three, four and five spins interacting with antiferromagnetic exchange interaction where the exchange interaction between one of the spins and the other spins may be different from the n-n exchange between the remaining spins placed in a ring. These systems provide a useful theoretical framework for calculating the magnetic properties of several recently synthesized molecular magnets.