On quantum spin chains and liquid crystal films

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Abstract
A two dimensional spin model introduced by Korshunov and by Lee and Grinstein, which describes ordering of molecules with competing nematic and ferromagnetic interactions, has been studied. Using the transfer matrix formalism, we have derived an equivalent spin 2 quantum model in one spatial dimension. This has been diagonalised for chains of finite length. We find behaviour consistent with the predicted phase diagram ; a low temperature planar phase separated from a disordered highs temperature phase by a line of transitions of the Kosterlitz-Thouless type, and from a low temperature nematic phase by a line of Ising transitions. The nematic to paramagnetic transition has also been predicted to be Kosterlitz-Thouless-like. Here the numerical evidence is less clear ; however we discuss topologies consistent with our results