Freezing temperature in disordered ferroelectrics

At low temperatures disordered ferroelectrics condense in mesoscopic structures, intermediate between dipole glass and regular ferroelectrics. We propose an approach for the evaluation of the freezing temperature of such mesoscopic structures based on the random local field theory (which partially takes into account the correlation effects) and the computer simulations. The problem reduces to the diagonalization of random matrix whose elements depends on the interaction and temperature. We identify the onset of freezing with the temperature at which the maximum eigenvalue of the matrix is equal to one. The corresponding eigenvector reproduces the low temperature structure.