FourthOrderParameter is used to detect an order-disorder transition. More...

#include <FourthOrderParameter.h>

Inheritance diagram for Pscf::Rp::FourthOrderParameter< D, T >:

Public Member Functions
void	setup () override
	Setup before the main loop.

Protected Member Functions
	FourthOrderParameter (typename T::Simulator &simulator, typename T::System &system)
	Constructor.
	~FourthOrderParameter ()=default
	Destructor.
double	compute () override
	Compute and return the order parameter.
void	computePrefactor (Array< double > &prefactor)
	Compute prefactor for each Fourier wavevector.

Protected Attributes
T::RField	prefactor_
	Prefactor for each Fourier component.
int	kSize_
	Number of wavevectors in Fourier space (k-grid) mesh.

Detailed Description

template<int D, class T>
class Pscf::Rp::FourthOrderParameter< D, T >

FourthOrderParameter is used to detect an order-disorder transition.

This class evaluates and averages the sum of fourth power of the magnitude of the Fourier mode amplitudes of a fluctuating exchange field for a binary system.

The order parameter is defined as

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

where \(W_({\bf G})\) is a Fourier mode of fluctuating field.

Specializations of this template are used as base classes for two closely analogous class templates, also named FourthOrderParameter, that are defined in the Rpc and Rpg namespaces for use in the pscf_rpc and pscf_rpg programs, respectively.

Template parameters:

D : dimension of space
T : Types class, Rpc::Types<D> or Rpg::Types<D>

See also: Manual Page

Definition at line 51 of file fts/analyzer/FourthOrderParameter.h.

Constructor & Destructor Documentation

◆ FourthOrderParameter()

template<int D, class T>

Pscf::Rp::FourthOrderParameter< D, T >::FourthOrderParameter	(	typename T::Simulator &	simulator,
		typename T::System &	system )

protected

Constructor.

Parameters

simulator	parent Simulator object
system	parent System object

Definition at line 30 of file FourthOrderParameter.tpp.

References kSize_, and Util::ParamComposite::setClassName().

◆ ~FourthOrderParameter()

template<int D, class T>

Pscf::Rp::FourthOrderParameter< D, T >::~FourthOrderParameter ( )

protecteddefault

Destructor.

Member Function Documentation

◆ setup()

template<int D, class T>

void Pscf::Rp::FourthOrderParameter< D, T >::setup ( )

override

Setup before the main loop.

Definition at line 42 of file FourthOrderParameter.tpp.

References computePrefactor(), Pscf::VecOp::eqS(), kSize_, prefactor_, and UTIL_CHECK.

◆ compute()

template<int D, class T>

double Pscf::Rp::FourthOrderParameter< D, T >::compute ( )

overrideprotected

Compute and return the order parameter.

Definition at line 69 of file FourthOrderParameter.tpp.

References kSize_, Pscf::VecOp::mulEqV(), prefactor_, Pscf::VecOp::sqSqAbsV(), Pscf::Reduce::sum(), and UTIL_CHECK.

◆ computePrefactor()

template<int D, class T>

void Pscf::Rp::FourthOrderParameter< D, T >::computePrefactor ( Array< double > & prefactor )

protected

Compute prefactor for each Fourier wavevector.

For the real-valued function W_, each Fourier coefficient G satisfies W_(G) = W_(-G). This function uses Brillouin Zone (BZ) indices representation. After applying fftw, if both the wavevector G and its inverse -G exist in k-space, the prefactor is assigned to be 1/2 for both G and -G. Otherwise, it is assigned to be 1.

Definition at line 100 of file FourthOrderParameter.tpp.

References Util::DArray< Data >::allocate(), Pscf::MeshIterator< D >::atEnd(), Pscf::MeshIterator< D >::begin(), kSize_, Pscf::Vec< D, T >::negate(), Pscf::MeshIterator< D >::position(), and Pscf::MeshIterator< D >::rank().

Referenced by setup().