Replica-Exchange Wang Landau Simulator

W. Joe Meese ~ meese022@umn.edu

Summary

This code base is a Replica-Exchange Wang Landau (REWL) simulator written to generalize the REWL method to various Hamiltonians smoothly. Once written, it will allow the user to only specify the details of a templated Hamiltonian and observables and remove the user from the nitty-gritty details of replica communication via MPI. In principle, this will allow quick development and study of different classical thermodynamic systems without the need for regular development of the actual algorithm itself.

This REWL_Simulator was first built to study the problem of random strain disorder in the unconventional superconductors known as the iron pnictides [Phys. Rev. B 106, 115134 (2022)]. If one should use this code for their own research, please cite that original paper. For convenience, here is the BibTeX entry:

@article{PhysRevB.106.115134,
  title = {Random strain induced correlations in materials with intertwined nematic and magnetic orders},
  author = {Meese, W. Joe and Vojta, Thomas and Fernandes, Rafael M.},
  journal = {Phys. Rev. B},
  volume = {106},
  issue = {11},
  pages = {115134},
  numpages = {22},
  year = {2022},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.106.115134},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.106.115134}
}

Code Basics

The goal for this code base is for it to be written in C++ and built with cmake across different platforms. Currently it has only been tested on Linux systems. This section will be updated as more of the code is developed.

System Requirements

The code base requires the std::filesystem which was officially adopted in the C++17 standard. It is recommended that a recent enough compiler is used, or else pieces of the filesystem will be scattered through the standard library in iomanip and std::experimental::filesystem, and so the compilation with make will fail. On Intel 64-bit systems, successful compilation is achieved with GNU 9.x and OpenMPI 4.x or newer.

Code Installation

First, clone this repo directly. Suppose the relative path to the clone is then repo_path. Then cd into that directory as cd repo_path. Next create a build directory within the cloned source. It is not recommended to build in-source! From the Unix terminal, execute the following

# After 'cd repo_path'
mkdir build
cd build
cmake ..
make -j

cmake will fail if an MPI implementation is not found. If it is, cmake will determine the correct MPI compiler and then the corresponding runtime flags. These will be outputted at the configure step of cmake and will be stored in the build/CMakeCache.txt file if the configure step is successful.

When make -j is called for parallel compilation, the simulation runtime executable will be stored in the build directory as bin/REWL_Simulator. The runtime command to execute the code will come down to

MPIEXEC MPIEXEC_NUMPROC_FLAG MPIEXEC_MAX_NUMPROCS MPIEXEC_PREFLAGS ./bin/REWL_Simulator MPIEXEC_POSTFLAGS <simulator-flags>

MPIEXEC MPIEXEC_NUMPROC_FLAG MPIEXEC_MAX_NUMPROCS MPIEXEC_PREFLAGS ./bin/REWL_Simulator MPIEXEC_POSTFLAGS <simulator-flags>

Currently, there are no runtime flags to be passed as <simulator-flags> to the simulation.

Build flags

Some cmake options to be aware of are as follows:

Global simulation control flags

MPI_ON
- This engages parallelization and replica exchange.
- This option is deprecated and will soon be mandatory.
COLLECT_TIMINGS
- This flag compiles the timing functionality through the C++ Standard Library (std::chrono).
PRINT_HISTOGRAM
- When set, the histograms are intermittently written to a file.
- Currently this is not thread safe and will be corrected as the parallelization is implemented.
REDUCE_LOGDOS
- This truncates the logDoS at the same time as the energy histogram such that the ground state value of the logDoS is zero. Since only differences in the logDoS affect the Monte Carlo moves, this is allowed.
- The idea here is to reduce the degree of numerical error saturation in calculating acceptance probabilities. When the logDoS gets too large, it will overflow the mantissa, especially when the incrementer is much smaller than the magnitude of the logDoS.
SAMPLE_AFTER
- This waits until one full round of REWL (or simply WL) has been completed before any sampling of the non-energetic observables is performed. By doing so, this guarantees that Detailed-Balance is more closely approximated for these statistical observables.
- For the second round of REWL moves with observable sampling, then the logDoS incrementer is reset back to one, and the simulation proceeds as it did before, only now it takes measurements concurrently.
TRAPEZOIDAL_RULE
- Evaluate the thermodynamic integrals with the trapezoidal rule.
- This will likely be absorbed into the main code in the future.
INDEPENDENT_WALKERS
- If engaged, there will be no replica exchange, nor will there be any intra-window walker averaging.
DIFFERENT_SEEDS
- Use different seeds for each walkers based on high-speed clock. If not engaged, then all seeds are identical.
EQUAL_WINDOWS
- This will make all the windows equally-sized with a well defined window size.
- One must be careful to make sure that each window is an integer number of bins or this simulation will break.
JOB_ARRAYS
- If engaged, the path-construction system will be changed to allow for many jobs.
- This will eliminate potential data over-write and allow for further averaging over the independent jobs to benefit the statistics.
CORRELATION_LENGTHS
- If engaged, the Fourier transform of the field correlator will be averaged in each energy bin periodically.
- At the end of the simulation the correlation lengths will be obtained via a combination of the correlator at q = 0 and q = 2pi / L.
SIMULATED_ANNEALING
- This will run a simulated annealing simulation at the beginning of the REWL simulation to determine the ground state energy and configuration.
- This is crucial for when the ground state is unknown.

Supported Hamiltonians

If multiple Hamiltonians are selected at build time, then cmake will throw a FATAL_ERROR.

ISING2D
- This flag sets the Ising model on a 2d square periodic grid.
- It is the default Hamiltonian used.
ASHKIN_TELLER2D
- This flag sets the Ashkin-Teller model on a 2d square periodic grid.
- Right now, the Ashkin-Teller model is supported within the ferromagnetic Baxter regime.

Hamiltonian Additions

These are add-ons to the Hamiltonians above.

RFIM
- This morphs the Ising model into a random-field Ising model.
RFAT_BAXTER
- This adds a random-field for the Baxter spin in the Ashkin-Teller model.

meese-wj/REWL_Simulator