Modular Landau Analysis of Coupled Phase Transitions: Application to Ferroelectric Liquid Crystals

Abstract

In systems with coupled order parameters, the relaxation of existing order can modify subsequent transitions, while cooperation and competition between emerging modes can produce complex phase sequences. We develop a modular Landau analysis that locally relaxes noncritical parent-phase variables to obtain effective one- and two-mode free energies. The resulting coefficients quantify relaxation-induced changes in transition characteristics and mode coupling, including changes in transition order for even-symmetry modes. The resulting modules are assembled successively along parent branches, and the equilibrium phase sequence is selected by comparing the fully relaxed free energies of the admissible branches. We apply the framework to ferroelectric liquid crystals, where orientational, polar, smectic, and tilt orders interact and give rise to multiple competing pathways, using a uniaxial model with longitudinal polarization. We fit the model to the measurements reported by Strachan et al. [Adv. Sci. 12(3), 2409754 (2025)]. A single thermodynamic parameter set reproduces the observed transition temperatures, transition types, and phase sequence, while capturing the main birefringence trend. Smectic layer spacing is reconstructed separately through a fitted observation map based on the calculated equilibrium tilt.