A Possible Phase Transition in beta-pyrochlore Compounds
  We investigate a lattice of interacting anharmonic oscillators by using a mean field theory and exact diagonalization. We construct an effective five-state hopping model with intersite repulsions as a model for beta-pyrochlore AOs_2O_6(A=K, Rb or Cs). We obtain the first order phase transition line from large to small oscillation amplitude phases as temperature decreases. We also discuss the possibility of a phase with local electric polarizations. Our theory can explain the origin of the mysterious first order transition in KOs_2O_6. 
Kazumasa Hattori and Hirokazu Tsunetsugu