Journal of statistical physics vol:100 issue:5-6 pages:829-851
Based on the l/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n --> infinity; limit of the local fluctuation field has faster large-distance correlation decay than its Hartree-Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree-Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree Fock prediction.