A fast parallel C++ program for various computations of the 2D Ising model. Example uses:

magneto -L=30 -TMax=6 -TSteps=10 -en=energy -mag=magnetization

For much more examples and things you can do with it, see the IPython Notebook.

Needs C++11, OpenMP and boost. Compile with make.

There is already a lot of Ising code out there, but most are sub-optimal for various reasons. Among those are slow performance, unreadable code, nonexistant documentation, missing normalization of the physics or missing observables. I hope this program does slightly better.

The grid size can be set with -L=32, the coupling constant J with -J=1, and the number of threads with -threads=3 (default=3). For performance reasons, J is parsed and used as an integer! But usually it's 1 or -1 anyways.

The temperatures can be controlled with the three parameters -TMin=0.1 -TMax=4.53 -TSteps=9. The odd default TMax value corresponds to twice the critical temperature. The interval is divided into TSteps steps. Note that start and endpoint are included! It's equivalent to NumPy's np.linspace(0.0, 3.0, num=4).

Besides the default uniform temperature distribution, they can also be generated with a normal distribution around the critical temperature. That helps to concentrate the computation around the interesting point. Use with -dist=normal. Minimum and maximum temperatures are always included, the space between is filled with a normal distribution with sigma=1.0.

The initial state can be set with -initial=random. Valid parameters are random, uniform (all +1), neel (antiferromagnetic or "checkerboard") or a filename. If a filename is given, that configuration is loaded. Important: set the grid length first (-L=50)! The format is expected to be ones and zeros with comma seperation. Example:

1,0,1
0,1,0
1,0,1

The algorithm that's used can be set with -alg=metro. Valid parameters are metro (Metropolis) and sw (Swendsen-Wang). The number of times that algorithm is run during equilibration can be controlled with -N1=50. After the equilibration phase, the number of steps for the main phase can be set with -N2=500 (works like above). The number of algorithm runs between each step is -N3=5.

The parameter -record=... controls when and how often measurements are written. By default (end), that's once at the end of the main phase. But they can also be recorded as a series during the main phase with -record=main. The number of written results is then N2.

Every measurement is written into a separate file. On each line, the output files contain the temperature followed by one or more results of the measurement at that temperature. The file is in csv format (=comma separated).

Energy and magnetization can be recorded with -en=filename and -mag=filename respectively. Those two are properties that can be measured on the system directly and are averaged during the main phase. With -record=main, the ith result is the average of all the previous measurements and therefore only the last value is averaged over N2. For the default -record=end setting, the result is just the average over the N2 measurements.

Heat capacity and magnetic susceptibility can be recorded with -cv=filename and -chi=filename respectively. They are measured from the variation in energy/magnetization (divided by the respective T and T^2 factors).

The correlation function can be recorded with -corr=filename. It's different in that it outputs not one, but L/2 values. They can be fitted externally to calculate the correlation length and the susceptibility from it. See the notebook for that.

System states can be recorded with -states=filename. The output is handled slightly different: A file is written for every temperature like filename0.txt, filename1.txt and so on. In the -record=end mode, the file format is like the initial state format:

1,0,1
0,1,0
1,0,1

With -record=main, the different states are written directly under each other. Example: Computation is started with magneto -TMin=2.5 -TSteps=1 -L=80 -measure=states -states=state. To plot with matplotlib: plt.imshow(np.loadtxt("state0.txt", delimiter=","), cmap=plt.cm.Greys, interpolation ="none"). Result: