I am doing a numerical simulation of the 2D-Ising model using the Metropolis algorithm. One of the plots that we were asked to make was Energy vs Monte-Carlo Steps for different starting Temperatures. My TA told me that irrespective of the starting temperature we should see the same equilibrium energy after large number of steps.
However, neither am I getting the same equilibrium energies at different temperature nor do I think that they should be the same. Since the Boltzman weight is higher for lower temperatures I should see higher energy values for lower temperatures is what my intuition is telling me.
And that is also the result that I'm getting- Plots. Is my TA wrong or am I missing something here