performs simulated annealing on the magnetic structure and measurements
at multiple parameter values
stat = ANNEALLOOP(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 DM
interactions are not supported yet!
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.
func Function that changes the parameters in the sw object in every
loop. Default function is to change the temperature:
@(obj,T)obj.temperature(T)
The function takes two input: sw objec and a parameter vector.
x Matrix of values of the loop parameter, with dimensions of
[nPar nStep]. Default is 1. In the i-th loop the loop function
is called as:
func(obj,x(:,i));
random Random initial conditions before the first loop, 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 loop. 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 end of each loop to calculate
statistical averages. 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 [default]
2 plots temperature changes and final report
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.
saveObj If true, the sw object is saved after every annealing step for
debugging purposes. Default is false.
title Gives a title string to the simulation that is saved in the
output.
Output:
stat A struct type data that contains the calculated thermodynamical
averages and the parameters of the simulation for evry value of
X with the following fields:
param All input parameter values of the annealloop 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.