This analyzer calculates the maximum amplitude of the second power of Fourier modes of exchange fields, referred to as the max order parameter. This analyzer is commonly used to identify order-disorder transition (ODT) that occur spontaneously during a transition, and to help classify states as ordered or disordered.

See also: MaxOrderParameter (class API)

Definition

Let \( \Psi\) denote the maximum square-magnitude of the Fourier coefficients of \( W_{-} \), such that

\[ \Psi \equiv \max_{\bf G} \left[ |W_{-}(\mathbf{G})|^{2} \right] \]

where \( \bf G \) denotes a wavevector used to compute a DFT, and the maximum is over all wavevectors.

Parameter file

Parameter file format:

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

Meanings of the parameters:

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

Output during a simulation:

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

If nSamplePerOutput == 1, or if this optional parameter is omitted, then the indices of the wavevector associated with the maximum Fourier amplitude are output along with corresponding value of \( \Psi \) every interval time steps or trajectory frames, with no block averaging.

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

Final output :

At the end of the 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.