# MFHUB

MFHUB is a very small and simple code that performs mean field calculations for
the two dimensional Hubbard model on a triangular lattice. It was written as an
exercise for the lecture "Computational methods in solid state theory" that I
attended during the summer term 2012 at the Goethe University of Frankfurt.

In order to understand what MFHUB does, I suggest that you take a look at the
corresponding lecture notes (itp.uni-frankfurt.de/~jeschke/CMSST/chapter6.pdf)
and the exercise (itp.uni-frankfurt.de/~jeschke/CMSST/exercise7.pdf)
that MFHUB attempts to solve.

Feel free to contact me with any questions (or bugs!) that come up!


## Building

Note: This section assumes that you have the GNU software development tools
like GCC, make and ld already installed on your machine.

Before building MFHUB make sure that you have installed its dependencies.
MFHUB distinguishes required and optional dependencies: While you don't need the
optional dependencies to build MFHUB, you will not be able to automatically
visualize your results without them.

required:

* [Eigen >3.1](https://eigen.tuxfamily.org/)
* [GNU scientific library](https://www.gnu.org/software/gsl/)

optional:

* [gnuplot](https://www.gnuplot.info)

Once you have the dependencies installed, building MFHUB is really simple and
straightforward:

    git clone git:https://github.com/robertrueger/MFHUB.git
    cd MFHUB
    make


## Command line arguments

    mfhub [uint s]
          [float t] [float t_prime] [float U]
          [uint N_SCC]
          [float m_prec] [uint max_iterations]
          [uint init] [float kT]
          [uint plotmode]          

  uint s
Sets the size of the system. MFHUB will internally treat the triagular lattice
as a square lattice with diagonal bonds, so the total number of sites in your
system will be s*s.

  float t, float t_prime, float U
Sets the Hamiltonian parameters. Note that t_prime and U are measured relative
to t, so it would be natural always to set t=1.

  uint N_SCC
Sets the total number of simulations performed by MFHUB. When using random
initial conditions not every self-consistency cycle will converge to the real
ground state, so you need to run many s.-c. cycles and select the one that yields
the lowest total energy: The correct ground state is the self-consistent
solution with the minimal energy!

  float m_prec
Sets the threshold for considerung a self-consistency cycle converged.

  uint max_iterations
Sets the maximum number of iterations until non-converged self-consistency cycles
will be aborted.

  uint init
Sets the initial mean-field parameters.
== 0: random within (0,1)
== 1: checkerboard
== 2: paramagnetic + initial Fermi-Dirac distributed (see lecture notes!)

  float kT
Sets the temperature used in the Fermi-Dirac distribution if init=2.

  float plotmode
Tells MFHUB which results to plot.
== 0: no plotting
== 1: plot best estimate of the ground state
== 2: plot all converged solutions


## License

Copyright (c) 2012, Robert Rüger <[email protected]>

MFHUB is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

MFHUB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with MFHUB.  If not, see <https://www.gnu.org/licenses/>.