performs simulated annealing on the magnetic structure
stat = ANNEAL(obj, 'option1', value1 ...)
The function can deal only with single ion anisotropy and isotropic
exchange interactions in 1, 2 or 3 spin dimensions.
General and antisymmetric exchage interactions are not supported yet!
Also the g-tensor is fixed to 2.
WARNING!
The calculated energies doesn't contain the self energy (moment coupled
to itself), thus the energies calculated here can differ from the
result of the sw.energy() function.
Input:
obj Input object contains structural data, sw type.
Options:
spinDim Dimensionality of the magnetic moments.
1 Ising spins
2 XY spins
3 Heisenberg spins [default]
For Ising (spinDim=1) and XY (spinDim=2) models only isotropic
exchange interaction and magnetic field can be used. For Ising
the direction of the spins are along x-axis, for XY model the
the xy-plane. Magnetic fields perpendicular to these directions
are omitted.
initT The initial temperature, can be any positive number,
unit is Kelvin. Default is 1.
endT Temperature at which to stop, can be any positive number
smaller than 'InitTemp', unit is Kelvin.
Default is 1e-3.
cool Generates a new temperature from the previous one.
Any function handle that takes a scalar as input and
returns a smaller but positive scalar as output.
Default is @(T) (.92*T).
random Random initial conditions, if initial spin configuration
is undefined (obj.mag_str.S is empty) the initial configuration
is automaticly random independently of the value of random.
Default is false.
nMC Number of Monte-Carlo steps per spin at each temperature
step to reach thermal equilibrium. Default is 100.
nORel Number of over-relaxation steps after every Monte-Carlo
steps. It rotates the spins around the direction of the local
field by 180deg. It is reversible and microcanonical if the
single ion anisotropy is zero. Default is 0.
nStat Number of cycles at the last temperature to calculate
statistical averages. It has to be smaller or equal nMC.
Default is 100.
boundary Boundary conditions of the extended unit cell.
'free' Free, interactions between extedned unit cells are
omitted.
'per' Periodic, interactions between extended unit cells
are retained.
Default is {'per' 'per' 'per'}.
verbosity Controls output to the screen.
0 suppresses all output
1 gives final report only
2 plots temperature changes and final report [default]
nExt The size of the magnetic cell in number of unit cells, to
provide input information to 'fStat'.
Default is from obj.mag_str.N_ext.
fStat Function handle to evaluate after at the end of the
cooling scedule during the last nStat Monte-Carlo steps.
The function returns a single structure and takes fixed
input parameters:
struct = fStat(state, struct, T, E, M, nExt).
The function is called once before the annealing process
when state=1 to initialise the parameters. The function
is called after every Monte-Carlo steps with state=2 and
the output of the previous function call is assigned to
the input struct. fStat is called once again in the end
with state=3 to calculate final parameters (in the last
run, input struct.param contains all the annealing
parameters).
Default is <a href="matlab: doc sw_fstat">@sw_fstat</a>.
fSub Function to define sublattices for Monte-Carlo speedup.
cGraph = fSub(conn,nExt), where cGraph is a (1,nMagExt) sized
vector, conn is a (2,nConn) size matrix and nExt is equal to
'nExt'. Default is <a href="matlab: doc sw_fsub">@sw_fsub</a>
subLat Vector that assigns all magnetic moments into non-interacting
sublattices, contains a single index (1,2,3...) for every
magnetic moment, size is (1,nMagExt). If undefined, the
function defined in 'fSub' will be used to partition the
lattice.
title Gives a title string to the simulation that is saved in the
output.
autoK Bin length of the autocorrelation vector. Should be a few times
smaller than nMC. Default is zero, no autocorrelation function
is calculated.
Output:
stat Struct that contains the calculated thermodynamical
averages and the parameters of the simulation with the
following fields:
param All input parameter values of the anneal function.
obj The copy of the input sw class obj with the final magnetic
structure.
M Components of the magnetisation after the last annealing
run, dimensions are [3 nMagExt].
E Magnetic energy of the system after the last annealing run.
T Final temperature of the sample.
Depending on the 'fStat' parameter, additional fields are included. Using
the default function (@sw_fstat) the following parameters are calculated:
avgM Average components of the magnetisation over nStat runs,
dimensions are [3 nMagExt].
stdM Standard deviation of the mgnetisation components over
nStat runs, dimensions are [3 nMagExt].
avgE Average system energy per spin over nStat runs, scalar.
stdE Standard deviation of the system energy per spin over
nStat runs, scalar.
Cp Heat capacity of the sample: (<E^2>-<E>^2)/kB/T^2.
Chi Magnetic susceptibility of the sample: (<M^2>-<M>^2)/kB/T.
Reference:
Kirkpatrick, S., Gelatt, C.D., & Vecchi, M.P. (1983). Optimization by
Simulated Annealing. _Science, 220_, 671-680.
See also SW, SW.OPTMAGSTR, SW_FSUB, SW_FSTAT.