Entropy of spin clusters with frustrated geometry

• We study frustrated spin clusters of various shapes and sizes on a triangular lattice.
• Ground-state energies and entropies are determined by exact enumeration.
• Infinite volume limit values of the energies and entropies are discussed.
• Effect of the spin value on the investigated properties is examined.
• Some interesting properties, such as magnetocaloric effect, are discussed.

Geometrically frustrated clusters of Ising spins of different shapes on a triangular lattice are studied by exact enumeration. The focus is laid on the ground-state energy and residual entropy behaviors as functions of the cluster shape and size, as well as the spin value. Depending on the cluster shape, the residual entropy density in approach to the thermodynamic limit can either vanish or remain finite and the dependence can be decreasing, increasing or non-monotonic. Nevertheless, the relative entropies normalized by the respective thermodynamic limit values turn out to be little sensitive to the spin value. Attention is drawn to magnetocaloric properties of systems of selected cluster shapes.