Glauber dynamics

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In statistical physics, Glauber dynamics is a way to simulate the Ising model (a model of magnetism) on a computer. It is a type of Markov Chain Monte Carlo algorithm.[1]

The algorithm[change | change source]

In the Ising model, we have say N particles that can spin up (+1) or down (-1). Say the particles are on a 2D grid. We label each with an x and y coordinate. Glauber's algorithm becomes:[1]

  1. Choose a particle at random.
  2. Sum its four neighboring spins. .
  3. Compute the change in energy if the spin x, y were to flip. This is (see the Hamiltonian for the Ising model).
  4. If flip the spin. That is if flipping reduces the energy, then do it.
  5. Else flip the spin with probability where T is the temperature.
  6. Display the new grid. Repeat the above N times.

This tries to approximate how the spins change over time. The fancy term is that it is part of nonequilibrium statistical mechanics, which roughly studies the time-dependent behavior of statistical mechanics.[1]

History[change | change source]

The algorithm is named after Roy J. Glauber, Nobel Prize winner and a Harvard physicist who worked at Los Alamos.[1]

Related pages[change | change source]

References[change | change source]

  1. 1.0 1.1 1.2 1.3 "Glauber's dynamics | bit-player". Retrieved 2019-07-21.