Ginzburg–Landau theory for higher order phase transition

► Ginzburg–Landau theory for higher order phase transition has been proposed. ► We have used Ehrenfest thermodynamics to classify orders of phase transitions. ► By Bogoliubov inequality our model Hamiltonian reduces to the free energy functional. ► Analytic continuation of the free energy functional preserves certain symmetry. ► Our developed model is tested for third and fourth order phase transitions. Ginzburg–Landau theory for studying phase transitions of higher order has been derived using coarse graining and lattice formulation within Ehrenfest thermodynamics. Our developed Hamiltonian leads directly to the functional of the system. We studied the evolution of the order parameter using our developed model equations for third and fourth order phase transitions. The periodic nature of the system can be likened to spatially varying periodic soliton/antisoliton lattice of holes in condensate. This is different from what one observes for any conventional solitary wave in the second order phase regime.