  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.
