Please use MATLAB or C ++ to code. Thank you!

2. Use Metropolis-Hastings Monte Carlo Method to Studv the Ising Model (70 points every lattice site i, a spin variable = +1 or-1 i.j Write a code to predict the equilibrated average spin -N161of a two-dimensional 31 by 31 spin lattice (N-961 total electrons). In the Hamiltonian of the Ising model shown above, J- 0.5 kgTo (where To-300 K and k is the Boltzmann constant) and u 0 (no external fields here) (i) Show convergence of the Hamiltonian H as you increase the number of iterations under T- 100, 200, 250, 300, 350, 400, 500, and 600 K. (ii Predict and plot o) vs. the number of iterations under T- 100, 200, 250, 300, 350 (iii) (iv) 400, 500, and 600 K. Then summarize the results in a plot for (a) vs. T. Explain the trend you observed in the (o) vs. Tprofile and determine the phase transition temperature Tphase when (a) sharply drops to zero Plot the equilibrated two-dimensional spin lattice states under each temperature considered above. You can use the red grid to represent the spin up state ( 1) and blue grid to represent the spin down state (o,-1), as shown above on the right