Phase transitions in systems with strain-induced coupling between two order parameters

Abstract

The effect of strain-induced order-parameter couplings on phase transitions is investigated for systems with two one-dimensional order parameters. Starting from the Landau free energy expression, the inclusion of bilinear and linear-quadratic couplings between strain and the two order parameters leads, after renormalisation, to bilinear and biquadratic forms of order-parameter coupling. In the case of bilinear couplings, it is shown that instead of two transition temperatures, T ₁ and T ₂ (T ₁ > T ₂), one observes a renormalised T _c near T ₁ and a crossover point near T ₂ This crossover is not symmetry breaking. In the case of biquadratic couplings, four different phases (O, I, II, III) corresponding to four different order-parameter solutions are identified. The path of phase transitions between the different phases in relation to the order-parameter coupling is discussed in terms of the movement of an equilibrium point in the vector space of the two order parameters.