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.