2-Dimensional Lattice Monte Carlo
Here is 2-D Lattice Monte Carlo code in FORTRAN,
along with an example INPUT file .
- Here is a worthwhile README file
- Here are example output files:
file1.out ,
file2.out ,
file3.out ,
file4.out .
- It has only a single near-neighbor interaction but you may alter
the sign of the interaction, i.e. make it ferromagnetic
(clustering-like) or antiferromagetic (ordering-like).
- It will run a series of temperatures: Tinitial
to Tfinal in steps of N, as seen in INPUT.
- Three lattices are allowed: square, triangular, and rhombohedral.
- Be aware of temperature scale: it is in UNITS of INTERACTION.
(For V=1, T from 0.1 to 10 maximum.)
Simulations on a Ferromagnet
For each lattice, determine the approximate transition temperature
for a ferromagnetic interaction by performing MC simulation for
numerous temperatures and plot E versus T.
- For each lattice, you must do this for a few increasing sizes of
the MC box, L. (We suggest L= 4, 8, 15, 16.)
- For each lattice, what should you calculate and plot for the various L size boxes
in order to establish the (non-)existence of a phase transition? Do it!
Why is E vs. T not a good one?
- Without doing any finite-size scaling analysis, you should be
able to get reasonable values for Tcritical from those plots.
- Because the output is basically T, E, M, dE, dM, ... for multiple
MC steps, the CLAMPS VIEWER may also be used for other analysis too.
Simulations on a Anti-Ferromagnet
For each square lattice, you may wish to try to determine the approximate
transition temperature for an ANTI-ferromagnetic interaction.
It is not always the same as the FM one.
- Try increasing sizes of the MC box, L (We suggest L= 4, 8, 15, 16)
and repeat the calculations and plots.
- What happens between odd and even values of L?
Improvements for Analysis
- Try incorporating the specific heat into the analysis.
Plot Cv vs. T and compare that to the dE vs. T from above.
Recall that specific heat is related to the variance of the Energy.
- How does the Cv help the analysis?
- One may also use the pair correlations (or susceptibility for magnetic
systems) to help analysis. When are pair correlations helpful?