I am basically trying to minimize the Landau-Ginzburg free energy. NLOPT is not working well in my case. The method that implements the initial conditions well may be the good one.
Free energy is defined wrt groups of microstates that are related in some way, eg same temperature or interface size or whatver. For it to be defined therefore you need to project the state space onto a parameter, usually for Ising this is the total magnetisation or the temperature but you have a lot of choices. To search along the order parameter for free energy minima by Bennet-Chandler acceptance ratio, or WHAM, or Wang-Landau would be a normal approach.
The best way to minimize a Landau-Ginzburg functional depends on the specific system, i.e. on the complexity of the functional to be optimized. First of all you should use a good method for numerical integration, quadrature methods are good for this. Then, if the number of variables or parameters to be optimized is not very large, function NMinimize from Mathematica software is generally a good option. Some a priori knowledge on the structure of the soultion is important to escape from metastable or spurius solutions, I mean: is the magnetic structure homogeneous ? modulated ? spiral ? this information is essential to constrain the volume of phase space in which to search for the solution of the specific problem. Symmetries from boundary conditions can simplify considerably the problem to be solved by the numeric method.
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