Programming a 2D Ising Model/The effect of system size

This is the sixth section of the Ising model experiment. You can return to the previous page, The effect of temperature, or jump ahead to the next section, Determining the heat capacity.

Scaling the System Size

Your plots from the previous section showed how the magnetisation and energy vary with temperature, and you should be able to see the onset of the phase transition. In this region, the energetic and entropic driving forces are of almost equal importance, and large fluctuations in the state of the system can take place. In fact, it is a characteristic of phase transitions that fluctuations within a system start to take place over very long ranges. This is a big problem in our simulation — so far, we only have 64 spins (or "atoms", if you prefer), so our system may not be big enough for these long ranged fluctuations to be correctly modelled.

TASK 6: Repeat the final task of the previous section for the following lattice sizes: 2×2, 4×4, 8×8, 16×16, 32×32. Make sure that you name each datafile that you produce after the corresponding lattice size! Write a Python script to make a plot showing the energy per spin versus temperature for each of your lattice sizes. Hint: the NumPy loadtxt function is the reverse of the savetxt function, and can be used to read your previously saved files into the script. Repeat this for the magnetisation. As before, use the plot controls to save your an SVG or PNG image of your plot and attach this to the report. How big a lattice do you think is big enough to capture the long range correlations?

This is the sixth section of the Ising model experiment. You can return to the previous page, The effect of temperature, or jump ahead to the next section, Determining the heat capacity.