For the final project in my computational physics class, I've built and will be presenting results for monte carlo simulations of phase transition in the three dimensional ising model. Using the metropolis algorithm, I've been able to graph the magnetism of the system after a long period of evolution against different starting temperatures and have been able to estimate the critical point of the three dimensional ising model.
Eg: Below are simulation results showing the relationship between the system parameter beta (=Temperature * Boltzmann's constant / interaction energy) and the magnetism of the system per each spin after equilibration.
(For each trial represented in the graph above, the system was iterated/perturbed using the metropolis algorithm 10,000,000 times from a fully magnetized state to get an equilibrium state and then perturbed 1,000 more times while statistics for the average magnetization per spin were taken. System size: 50^3 spins.)
I also want to calculate critical exponents, but I don't know much about them.
What critical exponents are “important” or relevant to the ising model simulation and what is the basic algorithm for determining them? Any introductory reading material on this issue would be much appreciated.