Thermodynamics of Third Order Phase Transition: A Solution to the Euler-Lagrange Equations

The thermodynamics expected of systems undergoing third order phase transition has been investigated by identifying the orders through the analytic continuation of the functional of the free energy, using Ehrenfest thermodynamic theory. We developed the Euler - Lagrange equations for the order parameter and the vector potential and solved them for the first time using well - known mathematical formulations.