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First order transition between magnetic order and valence-bond order in a 2 D frustrated Heisenberg model

We study the competition between magnetic order and valence bond order in a two dimensional (2D) frustrated Heisenberg model introduced some time ago (1981)) for which a configuration of dimers is known to be the ground state in a certain range of parameters. Using exact diagonalisation of small clusters, linear spin wave theory and Schwinger boson mean field theory, we show that the transition between the two types of order is first-order, and that it takes place inside the domain where magnetic long-range order is stable with respect to quantum fluctuations.