Third year CMP compulsory experiment/Locating the Curie temperature

This is the eighth (and final) section of the third year CMP experiment. You can return to the previous page, Determining the heat capacity, or go back to the Introduction.

You should have seen in the previous section that the heat capacity becomes strongly peaked in the vicinity of the critical temperature. You should have seen the heat capacity becomes increasingly sharply peaked as the system size was increased — in fact, Onsager proved that in an infinite system the heat capacity should diverge at $T = T_C$. The fact that our finite systems do not exhibit this divergence is evidence of a finite size effect.

It can be shown, however, that the heat capacity must scale according to $C_L = \frac{A}{L} + C_{\infty}$, where $C_L$ is the heat capacity of an $L\times L$lattice, and $C_\infty$ is the heat capacity of an infinite lattice, and $A$ is a constant in which we are not especially interested.

TASK: A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file is in the same format as the ones that you have produced, and you can read them with the NumPy loadtxt function as before. For each lattice size, plot the C++ data against your data. For one lattice size, save a PNG of this comparison and add it to your report — add a legend to the graph to label which is which. To do this, you will need to pass the label="..." keyword to the plot function, then call the legend() function of the axis object (documentation here).

This is the eighth (and final) section of the third year CMP experiment. You can return to the previous page, Determining the heat capacity, or go back to the Introduction.