def _plot_theoretical_l1(axes):
    """
    Plot the theoretical l1 phase transition on the `axes`.

    Parameters
    ----------
    axes : matplotlib.axes.Axes
        The matplotlib Axes instance on which the theoretical l1 phase
        transition should be plotted.

    Notes
    -----
    The plotted theoretical :math:`\\ell1` phase transition is based on
    tabulated values of available at
    http://people.maths.ox.ac.uk/tanner/polytopes.shtml

    """
    delta = [0, 0, 0, 0.001, 0.008, 0.021, 0.038, 0.058, 0.078, 0.1, 0.122,
        0.144, 0.167, 0.19, 0.212, 0.235, 0.258, 0.282, 0.305, 0.329, 0.352,
        0.375, 0.399, 0.422, 0.445, 0.468, 0.49, 0.513, 0.535, 0.558, 0.58,
        0.603, 0.626, 0.647, 0.669, 0.691, 0.712, 0.733, 0.754, 0.774, 
        0.794, 0.813, 0.832, 0.851, 0.868, 0.884, 0.9, 0.915, 0.929, 0.942,
        0.953, 0.963, 0.972, 0.98, 0.986, 0.991, 0.996, 0.998, 1]
    rho = [0, 0.025, 0.051, 0.077, 0.103, 0.125, 0.144, 0.16, 0.176, 0.19, 
        0.202, 0.215, 0.227, 0.238, 0.249, 0.26, 0.271, 0.282, 0.293, 0.304,
        0.315, 0.326, 0.337, 0.348, 0.359, 0.37, 0.381, 0.392, 0.404, 0.415,
        0.428, 0.44, 0.453, 0.466, 0.479, 0.493, 0.507, 0.522, 0.537, 0.552,
        0.568, 0.585, 0.602, 0.621, 0.639, 0.658, 0.678, 0.699, 0.721, 
        0.744, 0.767, 0.791, 0.815, 0.84, 0.864, 0.891, 0.921, 0.949, 1]
    axes.plot(delta, rho, c='k', ls='--', label='Theoretical $\\ell_1$')
