# Introduction to lattice models

## Random walks

If you know nothing at all about random walks, see the school kids' explanation. This is one of the easiest things to program, but there is help on how to set up your own simulation. See a random walk applet if you cannot do it on your own. Also, another applet for 2d random walks. Do you know why stock brokers are interested in random walks?

If you want to know more about Markov chains, your best bet is to go to the library and look under probability and statistics in the maths section. The web is not the best place to learn more, but if you insist, try a set of lecture notes, or a book in preparation.

## Percolation and random geometries

The best source material for percolation problems is D. Stauffer's article in Physics Reports. There is some online material by J. Wu at Berkeley, but it is short. Try also an introduction by computer.

## Spin models

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?

## Gauge theories

One of the best introduction to lattice gauge theory is the review paper by John Kogut in Reviews of Modern Physics, vol 51, p 659 (1979). See also the general references below.

## 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.