Equation of state and spin-correlation functions of ultrasmall classical Heisenberg magnets

We obtain analytical expressions for the total magnetic moment and the static spin-correlation functions of the classical Heisenberg model for ultrasmall systems of spins (unit vectors), that interact via isotropic, nearest-neighbor (n-n) exchange and that are subject to a uniform de magnetic field of arbitrary strength. Explicit results are presented for the dimer, equilateral triangle, square, and regular tetrahedron arrays of spins, These systems provide a useful theoretical framework for calculating the magnetic properties of several recently synthesized molecular magnets. The tetrahedron as well as the equilateral triangle systems, each considered for n-n antiferromagnetic exchange, are of particular interest since they exhibit frustrated spin ordering for sufficiently low temperatures and weak magnetic fields.