The Ising model is used here to simulate ferromagnetism. In this model, a two-dimensional (64 X 64) square array of interacting spin-1/2 particles at fixed temperature and magnetic field evolves in time. Each spin is pointing up or down (red or green). This lab examines the effect of temperature and an externally applied magnetic field on a system of spins. Below a critical temperature, with H = 0, ferromagnetic domains, or regions of local order, will appear.
The interaction described in the Ising model is only between nearest neighbor spins, and is -J for parallel spins and +J for antiparallel spins. The total energy can be expressed in the form
where si = ±1. The first sum is over nearest neighbor pairs of spins only. We designate that the external magnetic field H is in the up direction for positive values. The magnetization is just the number of up-spins minus the down-spins divided by the total number of spins.
To read more about the criteria for changes for each time step read about the Metropolis algorithm.
The exercises are divided as follows:
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Section 1 |
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Magnetization |
| Section 2 | Energy |
The Physlets contained in this exercise package was written by Wolfgang Christian . This lab was prepared by Dan Boye.