SpinW documentation

TEST2.

doctest2()

Summary line.

[b1, b2] = doctest2(a,b)

Extended description of function.

Parameters:
  • a1 – Description of arg1.
  • a2 – Description of arg2.
Returns:

  • b1 – Description of return value.
  • b2 – Other output.

Examples

This will calculate the spectrum:

doctest(1,2);
doctest(obj, varargin)

performs simulated annealing on the magnetic structure

The simulated annealing is performed using the Metropolis algorithm with parallel updating non-interacting sublattices. The function can deal with arbitrary exchange interactions, anisotropies in 1,2 and 3 dimensions.

stat = ANNEAL(obj, 'paramName', value1, ...)

Warning

The calculated energies doesn’t contain the self energy (moment coupled to itself), thus the energies calculated with this function can differ from the result of the energy() function. Also the g-tensor is fixed to 2.

Parameters:
  • obj – Input object contains structural data, sw type.
  • 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 value 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 value is:

    @(T) (.92*T)
  • random – Random initial conditions, if initial spin configuration is undefined (sw.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 180 \(^\circ\). 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 value 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 value is {'per' 'per' 'per'}.

  • verbosity –

    Controls output to the screen. Possible values:

    • 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 sw_fstat().

  • fSub –

    Function to define sublattices for Monte-Carlo speedup, with header:

    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 value is sw_fsub().

  • 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.
Returns:

stat – Struct that contains the calculated thermodynamical averages and the parameters of the simulation in the following fields:

fields definition
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:

fields definition
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: \((\langle E^2\rangle-\langle E\rangle^2)/k_B/T^2\).
Chi Magnetic susceptibility of the sample: \((\langle M^2\rangle-\langle M\rangle^2)/k_B/T\).

Return type:

struct

Example

The following example does annealing on a triangular lattice:

model1 = sw_model('triAF',1);
model1.anneal;

References

S. Kirkpatrick, et al., “Optimization by Simulated Annealing”, Science, 220, 671 (1983).

Indices and tables