Pseudo-critical slowing down within the cluster variation method and the path probability method

The pseudo critical slowing down phenomenon reported for an order-disorder transition of the first order is reproduced by the path probability method calculations on a L1₀ ordered phase. The slowing down takes place towards the instability temperature of the metastable ordered phase rather than the transition temperature. In order to clarify the thermodynamic origin of the pseudo critical slowing down, the temperature dependency of generalized susceptibilities are calculated for the L1₀ ordered phase as a function of v_2,2/v_2,1, where v_2,n is the nth nearest neighbour effective pair interaction energy. The diverging behaviour is observed towards the instability temperature through the transition temperature. This is pronounced, as the second-order character is emphasized. It is confirmed that the pseudo-critical slowing down phenomenon is caused by the flattening of the free energy surface, leading to the loss of the thermodynamic driving force for relaxation. The first-principles calculation of the susceptibility is attempted for Cu-Au system at a 1:1 stoichiometric composition. A sharp rise is confirmed near the transition temperature.