I'm working on a Magnetization simulation and writing an algorithm using the metropolis method.
I am using a change in energy and a Boltzmann distribution, but, my question is about the trial step. Should the trial position of the magnetization be completely random or should it be a random differential added onto the position of the old magnetization?
My energy basically depends on an angle, so, my range is 0 to Pi, and to get anything near a 50% rejection I'm adding or subtracting approximately pi over 4 from each step - which is far too large. If I reduce it to something reasonably small, then the difference in energy between the old and new energy probability is about 0.999 to 1.001. (here I create a random, small angle and add or subtract it from the current angle of the magnetization vector.)