.. _sphx_glr_api_gallery_statphys_ising:

Ising model
-----------

The 2D ferromagnetic Ising model: Onsager's exactly solved second-order phase
transition.


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


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

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    <div class="sphx-glr-thumbcontainer" tooltip="The 2D Ising model places a spin s_i = \pm 1 on every site of a periodic L \times L lattice, with Hamiltonian">

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  .. image:: /api/gallery/statphys/ising/images/thumb/sphx_glr_plot_critical_slowing_down_thumb.png
    :alt:

  :doc:`/api/gallery/statphys/ising/plot_critical_slowing_down`

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      <div class="sphx-glr-thumbnail-title">Critical slowing down: Metropolis vs. the Wolff cluster algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A single finite lattice can only show a rounded phase transition -- true singularities require an infinite system. Finite-size scaling theory turns this apparent limitation into a tool: by simulating several lattice sizes and comparing how observables scale with L, the exponents of the infinite system can be extracted without ever simulating one.">

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  .. image:: /api/gallery/statphys/ising/images/thumb/sphx_glr_plot_finite_size_scaling_thumb.png
    :alt:

  :doc:`/api/gallery/statphys/ising/plot_finite_size_scaling`

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      <div class="sphx-glr-thumbnail-title">Finite-size scaling: extracting critical exponents</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Away from T_C, the 2D Ising lattice&#x27;s equilibrium configurations look qualitatively different above and below the transition: a fine, short-range-correlated speckle in the disordered phase, or a few large, slowly fluctuating domains in the ordered phase. Exactly at T_C, neither picture applies -- the correlation length">

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  .. image:: /api/gallery/statphys/ising/images/thumb/sphx_glr_plot_ising_criticality_animation_thumb.png
    :alt:

  :doc:`/api/gallery/statphys/ising/plot_ising_criticality_animation`

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      <div class="sphx-glr-thumbnail-title">Watching criticality: the Ising lattice at T_C</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The 2D Ising model places a spin s_i = \pm 1 on every site of a periodic L \times L lattice, with Hamiltonian">

.. only:: html

  .. image:: /api/gallery/statphys/ising/images/thumb/sphx_glr_plot_ising_phase_transition_thumb.png
    :alt:

  :doc:`/api/gallery/statphys/ising/plot_ising_phase_transition`

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      <div class="sphx-glr-thumbnail-title">Onsager's exact solution: the 2D Ising phase transition</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/statphys/ising/plot_critical_slowing_down
   /api/gallery/statphys/ising/plot_finite_size_scaling
   /api/gallery/statphys/ising/plot_ising_criticality_animation
   /api/gallery/statphys/ising/plot_ising_phase_transition