.. _ug_tb_sh_3-2:

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

Second type of the trilinear terms, in which two spin operators are associated with the
same site, and the third one is associated with a different site. In this page we imply
that :math:`\boldsymbol{r}_{\mu,\alpha_1} \neq \boldsymbol{r}_{\mu + \nu_2, \alpha_2}`.

.. math::
    C_{3,2}
    \sum_{\substack{\mu, \nu_2, \\ \alpha_1, \alpha_2, \\ i_1, i_2, i_3}}
    \Biggl(
        &
        J^{i_1, i_2, i_3}_{0, \nu_2; \alpha_1, \alpha_1, \alpha_2}
        S_{\mu, \alpha_1}^{i_1}
        S_{\mu, \alpha_1}^{i_2}
        S_{\mu + \nu_2, \alpha_2}^{i_3}
        +\\&+
        J^{i_1, i_2, i_3}_{\nu_2, 0; \alpha_1, \alpha_2, \alpha_1}
        S_{\mu, \alpha_1}^{i_1}
        S_{\mu + \nu_2, \alpha_2}^{i_2}
        S_{\mu, \alpha_1}^{i_3}
        +\\&+
        J^{i_1, i_2, i_3}_{\nu_2, \nu_2; \alpha_1, \alpha_2, \alpha_2}
        S_{\mu, \alpha_1}^{i_1}
        S_{\mu + \nu_2, \alpha_2}^{i_2}
        S_{\mu + \nu_2, \alpha_2}^{i_3}
    \Biggr)

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

*   :py:attr:`magnopy.Convention.c32`

    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.p32`

    An iterator over the parameters already added to the Hamiltonian.