Glauber dynamics
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]
- Choose a particle at random.
- Sum its four neighboring spins. .
- Compute the change in energy if the spin x, y were to flip. This is (see the Hamiltonian for the Ising model).
- If flip the spin. That is if flipping reduces the energy, then do it.
- Else flip the spin with probability where T is the temperature.
- 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]
- ↑ 1.0 1.1 1.2 1.3 "Glauber's dynamics | bit-player". Retrieved 2019-07-21.