This is the library for computing equilibrium energy of magnetic hopfions
and other states of a classical helimagnet with the energy density

  E = Eex + Ez + Ea + Edm + Ems

where
 M = {Mx[X, Y, Z], My[X, Y, Z], Mz[X, Y, Z]}
 Eex = C/2 Sum[Grad[M[[i]], {X, Y, Z}]^2, {i, 1, 3}]
 Ez = - H Mz[X, Y, Z]
 Ea = - K Mz[X, Y, Z]^2
 Edm = D M.Curl[M, {X, Y, Z}]
and Ems is the self-energy of interacting volume charges with the density
 rho = Div[M, {X, Y, Z}]
whose total energy is a double-volume integral
 mu0 Ms^2 1/2 1/(4Pi) Integrate[rho[X1,Y1,Z1] rho[X2,Y2,Z2] /
    Sqrt[(X1-X2)^2+(Y1-Y2)^2+(Z1-Z2)^2], {X1,-LX,LX}, {Y1,-LY,LY},
    {Z1,-LZ,LZ}, {X2,-LX,LX}, {Y2,-LY,LY}, {Z2,-LZ,LZ} ]
where the integration is done over the unit cell of the hopfion lattice.

If the total energy per unit volume is normalized by mu0 Ms^2, the
problem turns out to have three independent dimensionless parameters:
q = 2 K C/D^2, h=mu0 Ms H C/D^2 and mu^2 = mu0 Ms^2 C/D^2. The small values
of mu correspond to negligible magnetostatic energy since mu^2 enters the
normalized energy density as a prefactor to Ems.

The hopfion variational model is defined in [Physica D 443, 133561 (2023)].
It depends on the hopfion radius R (embedded in the dimensionless parameter
nu = C/(D R) of the normalized energy density) and a function 0<f(x)<1, 
describing the hopfion profile as a function of the dimensionless radial
variable x=r/R .

The compilation was tested using gcc and gfortran, it also requires libreadline
headers to be installed. After running a successful make, the binaries are
built in the __bin_XXX directory, corresponding to your architecture (most
commonly "_bin_x86_64") under the checkout root.

There are three executables:

TEST      -- runs the testsuite and reports the number of successful and failed
             tests.

HOPFSHELL -- interactive program for exploring the phase diagram in h, q, mu
             space and creating initial states for phase diagram tracer. To
             see the list of commands, type help (or just "h") in the prompt.

PHB_TRACE -- non-interactive (although with optional fancy progress indicator)
             config-driven phase diagram boundary tracer. The examples of
             the config files are in ./examples/ directory.



(c) 2023 Konstantin L. Metlov <metlov@donfti.ru>

This program is free software: you can redistribute it and/or modify
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.

This program 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 can find the text of the GNU General Public License is in the LICENSE file.
If not, see <https://www.gnu.org/licenses/>.