This analyzer calculates the sum of fourth power of exchange field in fourier mode, referred to as the fourth order parameter. This analyzer is commonly used to identify order-disorder transition (ODT) in systems where the spontaneous phase transitions occur. In disordered phase, the fourth order parameter approaches to 0. In ordered phase, the fourth order parameter is a finite value.

See also: FourthOrderParameter (class API)

Mathematical Formula

\[ \Psi_{\text{fourth}} \equiv \left[ \sum W_{-}(\bf G)^4 \right] ^{\frac{1}{4}} \]

where \( \Psi_{\text{fourth}}\) denotes fourth order parameter, \( W_{-}(\bf G)\) denotes the Fourier components of the exchange field, and \(\bf G\) denotes the Fourier wavevector. The Fourier transformation is defined in Appendix: Periodic Functions and Fourier Series.

Parameter File

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

FourthOrderParameter{
  interval           int
  outputFileName     string
  hasAverage*        bool     (default true)
  nSamplePerBlock*   int      (default 1)
}

Meanings of the parameters are described briefly below:

Label	Description
interval	number of steps between data samples
outputFileName	name of output file
hasAverage	whether the average and error analysis are needed?
nSamplePerBlock	number of samples per block average

Output

During the simulation, \(\chi_b N \) and fourth order parameter are output to the file {outputFileName} every interval simulation steps.

At the end of the simulation, if hasAverage is true:

average and error analysis info are output to log file.