Glauber dynamics


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

The algorithm

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

History

The algorithm is named after Roy J. Glauber.

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