I am working on the Metropolis-Montercarlo algorithm for the square lattice ising 2D. Im running the simulations for a given lattice size, running from low temperature to high temperature, and getting for example, the magnetization vs Temp of the lattice. I get a set of data points that, in my supossition, are adjustable by a sigmoid or the inverse tangent function. I know I just can't fit a dataset of points with a given function. I must have a model behind that function to justify fitting them. Is there any theory (mean field, onsager) that one gets the magnetization vs the temperature?
This are some of my data set, and the sigmoid fitting I tried.
On the Y axis, there is the Spin per lattice site and in the X axis is temperature.
Sorry for the Spanish figures, im on the phone and access the Before You ask, the fluctuations near $"T_c"$ are still there, even when i do a lot of iterations.