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[en] The authors investigate the phase diagram of ferromagnetic Ising spin systems satisfying the G.H.S. inequality. They show that such systems cannot have a ''normal'' first-order phase transition as the temperature T is varied, i.e., one where the magnetization is discontinuous and there are three coexisting phases. Furthermore, for N.N. interactions, discontinuity in the magnetization at 0 < T0 ≤ T/sub c/ implies an uncountable infinity of pure phases at T0
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