.. _ug_tb_sh_3-3:

************
(3, 3) terms
************

Third type of the trilinear terms, in which all three spin operators are associated with
different sites. In this page we imply that :math:`\boldsymbol{r}_{\mu,\alpha_1}`,
:math:`\boldsymbol{r}_{\mu + \nu_2, \alpha_2}`, and
:math:`\boldsymbol{r}_{\mu + \nu_3, \alpha_3}` are all different.

.. math::
    C_{3, 3}
    \sum_{\substack{\mu, \nu_2, \nu_3 \\ \alpha_1, \alpha_2, \alpha_3 \\ i_1, i_2, i_3}}
    J^{i_1, i_2, i_3}_{\nu_2,\nu_3; \alpha_1,\alpha_2,\alpha_3}
    S_{\mu, \alpha_1}^{i_1}
    S_{\mu + \nu_2, \alpha_2}^{i_2}
    S_{\mu + \nu_3, \alpha_3}^{i_3}


Relevant API
============

*   :py:attr:`magnopy.Convention.c33`

    Convention constant.

*   :py:meth:`magnopy.SpinHamiltonian.add`

    Method to add the parameter to the Hamiltonian.

*   :py:meth:`magnopy.SpinHamiltonian.remove`

    Method to remove the parameter from the Hamiltonian.

*   :py:attr:`magnopy.SpinHamiltonian.p33`

    An iterator over the parameters already added to the Hamiltonian.