..
   Generated automatically by cpp2rst

.. highlight:: c
.. role:: red
.. role:: green
.. role:: param


.. _triqs_ctseg__evaluate_3w_vertex:

triqs_ctseg::evaluate_3w_vertex
===============================

*#include <triqs_ctseg.hpp>*



**Synopsis**

 .. rst-class:: cppsynopsis

       | void :red:`evaluate_3w_vertex` (block_gf<triqs::gfs::imfreq> const & :param:`gw`,
       |                     block_gf<triqs::gfs::imfreq> const & :param:`fw`,
       |                     gf_3w_container_t const & :param:`g3w`,
       |                     gf_3w_container_t const & :param:`f3w`,
       |                     bool :param:`measure_g3w`,
       |                     bool :param:`measure_f3w`,
       |                     std::string :param:`fname`)





 Evaluation of the 4-leg vertex for the 4-point correlation function
If one or two of the three-frequency correlation functions have been measured
 and the parameter ``evaluate_vertex`` is set to ``true``, the following vertex
 function is computed at the end of the simulation:



.. math::
		\gamma_{\sigma\sigma'}(i\omega,i\omega',i\nu) =
 \frac{G^{2,\text{con}}_{\sigma\sigma'}(i\omega,i\omega',i\nu)}{G_\sigma(i\omega)G_\sigma(i\omega+i\nu)G_\sigma'(i\omega'+i\nu)G_\sigma'(i\omega')}

..

Depending on which two-frequency correlation functions have been measured, the
 connected part is computed in either of the following ways:




.. math::
		G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) =
 G^{2}_{\sigma\sigma'}(i\omega,i\omega',i\nu) -
 G^{2,\text{disc}}_{\sigma\sigma'}(i\omega,i\omega',i\nu)

..




.. math::
		G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) = G_\sigma(i\omega)
 F_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)-F_\sigma(i\omega)
 G_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)

..




.. math::
		G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) = \Big[G_\sigma(i\omega)
 F_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)-F_\sigma(i\omega)
 G_{\sigma}^{2,\text{disc}}(i\omega,i\omega',i\nu)\Big]/[1+F_\sigma(i\omega)].

..

The disconnected part of the correlation function has been defined as



.. math::
		G^{2,\text{disc}}_{\sigma\sigma'}(i\omega,i\omega',i\nu) = \beta
 G_{\sigma}(i\omega)G_\sigma'(i\omega')\delta_{\nu}-\beta G_\sigma(i\omega)
 G_\sigma(i\omega+i\nu)\delta_{\omega,\omega'}\delta_{\sigma\sigma'}.

..