Abstract
We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interaction which frustrate each other. The system undergoes phase changes when the ratio between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of in the S = 1/2 case. For S = 1/2 we show that there are three ground-state phases, and determine their boundaries.
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