I have a structure at the ground-state exhibiting different random regions of FM and AFM arrangements, how to calculate the curie temperature knowing that calculating 'J' is not applicable?
Calculating the Curie temperature for a system with domain magnetization and different random regions of FM and AFM arrangements can be challenging. The Curie temperature is typically determined by analyzing the behavior of the magnetic susceptibility as a function of temperature. However, in your case, calculating the exchange coupling constant 'J' might not be applicable so an alternative approach you can consider is to do a thermal Monte Carlo simulations. One way to estimate the Curie temperature is by performing thermal Monte Carlo simulations on your system. The idea is to simulate the behavior of the system at different temperatures and observe the onset of magnetic ordering. At temperatures below the Curie temperature, the system will exhibit long-range magnetic order.