This analyzer calculates the sum of fourth power of Fourier amplitudes for the exchange field \( W_{-}({\bf r}) \), referred to as the fourth order parameter. Changes in this quantity may be used to identify spontaneous order-disorder transitions (ODT) that occur during a simulation.

See also: FourthOrderParameter (class API)

Definition

Let \( \Psi\) denotes the fourth order parameter,

\[ \Psi \equiv \left[ \sum_{{\bf G}} |W_{-}(\bf G)|^4 \right]^{1/4} \]

in which \( W_{-}(\bf G)\) denotes a Fourier components of the exchange field associated with wavevector \(\bf G\). The Fourier transformation is defined in Periodic Functions and Fourier Series.

Parameter file

The full parameter file format, including all optional parameters, is shown below:

FourthOrderParameter{
  interval*          int      (1 by default)
  outputFileName     string
  nSamplePerBlock*   int      (1 by default 1)
}

Meanings of the parameters are described briefly below:

Label	Description
interval*	number of steps between data samples
outputFileName	name of output file
nSamplePerBlock*	number of samples per block average output to file

Output

In the following, the symbol "{outputFileName}" is used to represent the string value of the outputFileName parameter within descriptions of output file names.

Output during a simulation or trajectory file analysis :

If nSamplePerOutput > 1, then block average values of \( \Psi \), averaged over blocks of nSamplePerOutput sequential samples, are output to the file {outputFileName}.dat every interval * nSamplerPerBlock simulation steps or trajectory file frames.

If nSamplePerOutput == 1 (or if this optional parameter is omitted), then values of \( \Psi \) are output every interval time steps, with no block averaging.

If nSamplerPerBlock = 0, then {outputFileName}.dat data file is not created.

Final output :

At the end of a simulation or trajectory file analysis:

The sequence average of \( \Psi \) and an estimated error on this average are output to the file {outputFileName}.ave
Details of the error analysis are output to the file {outputFileName}.aer

See the discussion of error analysis for further details.