Glauber dynamics

In statistical physics, Glauber dynamics^[1] 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.^[2]

The algorithm[]

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:^[3]

1. Choose a particle ${\displaystyle \sigma _{x,y}}$ at random.
2. Sum its four neighboring spins. ${\displaystyle S=\sigma _{x+1,y}+\sigma _{x-1,y}+\sigma _{x,y+1}+\sigma _{x,y-1}}$.
3. Compute the change in energy if the spin x, y were to flip. This is ${\displaystyle \Delta E=2\sigma _{x,y}S}$ (see the Hamiltonian for the Ising model).
4. Flip the spin with probability ${\displaystyle e^{-\Delta E/T}/(1+e^{-\Delta E/T})}$ where T is the temperature.
5. Display the new grid. Repeat the above N times.

History[]

The algorithm is named after Roy J. Glauber.^[2]

Related pages[]

• Metropolis algorithm
• Ising model
• Monte Carlo algorithm
• Simulated annealing

References[]