.. _ug_tb_sh_2-2:

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

Second type of the bilinear terms, in which spin operators are associated with different
sites. In other words, for these terms
:math:`\boldsymbol{r}_{\mu,\alpha_1} \neq \boldsymbol{r}_{\mu + \nu_2, \alpha_2}`.

.. math::
    C_{2, 2}
    \sum_{\substack{\mu, \nu_2, \\ \alpha_1, \alpha_2, \\ i_1, i_2}}
    J^{i_1, i_2}_{\nu_2; \alpha_1, \alpha_2}
    S_{\mu, \alpha_1}^{i_1}
    S_{\mu + \nu_2, \alpha_2}^{i_2}

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

*   :py:attr:`magnopy.Convention.c22`

    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.p22`

    An iterator over the parameters already added to the Hamiltonian.