2DRandomIsing

Code for calculating the Renyi entanglement entropy in the 2D Ising model with arbitrary couplings.

Parameter file

The way the code is currently structured is most clearly seen by looking at the parameter file, param.dat

Lattice_size_L 16
Disorder_prob_P 0.02
Random_seed 12345
Sweeps_per_bin 1000
Num_bins 100
Strips_in_regionA 0
reverse 0

The Lattice_size_L determines the size of the lattice, so it is LxL in the end. The Disorder_prob_P determines what fraction of the bonds are antiferromagnetic. This setting is overridden if the file LOADJ is present, in which case the program loads the couplings from Jmat.dat in the same directory as the executable. The Random_seed seeds the Mersenne Twister random number generator. A sweep in the program corresponds to

1. Nspins single spin updates
2. One cluster update
3. One measurement of the energy updateE()
4. One measurement of the ratio of partition functions updateRatio()
5. num_temps swap attempts for randomly chosen adjacent temperatures for parallel tempering

Num_bins is the number is the number of total bins, each one a single measurement in the file, and each bin is compried of Sweeps_per_bin sweeps and measurements. Strips_in_regionA describes how many Lx1 strips of spins are in region A. If this is set to zero, the two system are disconnected, and updateRatio() is measuring Z[A,2,T]/Z^2[T] where A is the first strip of spins, i.e. the spins from index 0 to index L-1. To measure the next strip (spins from index L to index 2L-1) we only change the param file such that Strips_in_regionA is 1. The largest sensible value for Strips_in_regionA is L-1, since in this case updateRatio() will measure the ratio of adding the last strip of spins. If we tried setting Strips_in_regionA to L, this would cause the code to error unless updateRatio() was turned off. Lastly, reverse determines whether we are building up region A from index 0 of the lattice or from index L*L-1. Both are needed to calculate the mutual information.

Basic run cycle of the code

The basic procedure for running the code (as I have been so far) is the following:

1. Create all the Jmat.dat files needed for simulation. If only +-1 values are needed, this can be done by running the code with the file SAVEJ present in the same location as the executable.
2. Choose the temperatures to simulate, and put these in temps.dat. Temps.py has an example script for creating evenly spaced beta points.
3. For each realization of disorder (or Jmat.dat file):
4. Run a simulation for each valid value of Strips_in_regionA. These run from 0 to L-1
5. For each value of Strips_in_regionA, we must run once with reverse set to 0, and once with reverse set to 1

This means, for each realization of disorder, we need to run the code 2L times, with each run internally containing num_temps simulations. Each simulation will create data files according to the beta used for each simulation. The data one is left with is samples of Z[A',2,T]/Z[A,2,T] where A is specific in the parameter file, and A' is region A plus one more strip.

This value is stored directly, so in larger systems there may be problems with numerical overflow that require some slight modifications

To calculate the mutual information, one must calculate as usual

I_2(A:B) = S_2(A) + S_2(B) - S_2(A \union B)

S_2(A) = \sum_{A_i=0}^{A_i+1=A} log[Z[A_i+1,2,T]/Z[A_i,2,T]]

i.e., if we want to calculate S_2(A) for the half strip, we have to take the sum of the logs of Z[A_i+1,2,T]/Z[A_i,2,T] for the first L/2 simulation. A concrete example -- with L=8, this will be the product of the simulations with Strips_in_regionA set from 0..3 (so 4 total simulations). To calculate S_2(B), we use the complimentary number of simulations with reverse set to 1. Again, for L=8, if we wanted to calculate S_2(A) for the quarter region, we would use the firt 2 simulations with reverse set to 0 (this would be 0 and 1) and the first 6 simulations with reverse set to 1 (0..5) The final value S_2(A \union B) can be calculated from the simulations with reverse set to either 0 or 1, it makes no difference, and in my processing I usually symmetrize over both methods to reduce error.

I usually organize runs by: REVERSE/DISORDER/REGION_A but any reordering of that should work just as well.

Getting started

Using the following scripts to test the code. Please note, the scripts are organized for use on a cluster, that means jobs are submitted through sqsub and we tar the final results to keep things organized (plus, some clusters have file number restrictions, and this circumvents that problem). It is also set up in such a way that the number of jobs submitted to the cluster simultaneously is never too many. After crashing a cluster once with 80,000 jobs, such measures are necessary.

• Compile the code (with make) -- you should get an executable called Ising.out.
• Move into to the directory sharcnet_test.
• Copy Ising.out into the this folder.
• Type python makedirs.py -- this will create two folders based on the size inside the file SIZE.
• Go into the two folders (called L#/ and L#r/) and run the command python submit_sharcnet.py -- this will submit the actual jobs, and is currently hardcoded to only submit 200 at a time. Running the command again will submit the next 200 jobs, and so on and so on.
• When the jobs are finished (or even when each batch is finished -- either is ok), run the command . ./tar_stuff in each of the L folders -- this will create data.tar containing all the simulation data for that set.
• Once all the jobs are complete, in the folder sharcnet_test run the command python analyze_MI.py -- this will create MI_L#.dat and MIE_L#.dat containing the mutual information and error. Each line is a temperature (it matches up with temps.dat) and each column is a different size of region A. The middle column is for the half cut.
• Finally, running python plot_MI.py will produce a crude plot.

Currently the files are setup to do a quick test of L=4 with only 16 realizations of disorder. The system size can be changed by modifing the number in the file SIZE (don't change the first part in the file) and the number of disorders must be changed in the following files (and it must be the same for all of them currently)

• analyze_MI.py
• genJs.py
• submit_sharcnet.py