.. _sphx_glr_api_gallery_statphys_percolation:

Percolation
-----------

Site and bond percolation: a purely geometric critical phenomenon.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Percolation theory shows that a sharp, universal phase transition does not require energy, temperature, or even dynamics -- pure geometry suffices. As the occupation probability p of a random lattice increases past a critical threshold p_c, an infinite spanning cluster suddenly appears. This example uses Hoshen-Kopelman cluster labeling to estimate the spanning probability curve P_{\text{span}}(p) for site percolation on the square lattice (p_c \approx 0.593), and visualizes the fractal, self-similar spanning cluster right at criticality.">

.. only:: html

  .. image:: /api/gallery/statphys/percolation/images/thumb/sphx_glr_plot_percolation_threshold_thumb.png
    :alt:

  :doc:`/api/gallery/statphys/percolation/plot_percolation_threshold`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Percolation: a purely geometric phase transition</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/statphys/percolation/plot_percolation_threshold