Long Range Orders on the Classical Bilinear-Biquadratic Exchange Hamiltonian

Abstract

Through the method of reflection positivity, we prove the existence of long range order associated with dipoleand quadrupole moments at finite temperature on the classical bilinear-biquadratic exchange Hamiltonian.We also obtain an upper bound on the dipole phase transition temperature, and find that there is a range of bilinear and biquadratic exchange interaction parameters for which the quadrupole phase transition temperature lies above the dipole one.