# The Ising model

## The model

See a simulation of the 2d Ising model which allows you to change the temperature of the system. Notice how the size and shape of clusters of spins change across the phase transition. Also see a Potts model applet which allows you to change the number of states, and the simulation algorithm. See how the Wolff algorithm changes configurations much faster than the Metropolis algorithm. The 2d Potts model has a second order phase transition only when the number of states is less than or equal to 4. Is this obvious when looking at the simulation? Why?

## Series expansion

See the high temperature series expansion for the Ising susceptibility. Analyse it to find the critical index gamma in 2d and 3d. Check whether the 3d value is the same as the experimentally determined value for liquid-gas, ferromagentic, binary mixture or micelle systems. The Ising model we have studied has only two states, and is called the spin 1/2 Ising model. Generally a spin S Ising model has 2S+1 states. See the low temperature series for spin S Ising models. Find the critical exponents.

## General References

*Exactly solved models in statistical mechanics*by R. J. Baxter*Statistical field theory*by C. Itzykson and J.-M. Drouffe*Equilibrium statistical physics*by M. Plischke and B. Bergersen*Quantum fields on the computer*by M. Creutz*Field Theory, the Renormalization Group and Critical Phenomena*, by D. Amit, World Scientific, Singapore, 1984.

© Sourendu Gupta. Created on Dec 29, 2001.