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The Potts model [#!POTTS!#,#!WU!#] encompasses a number of problems in
statistical physics and lattice theory. It generalizes the
Ising model so that each spin can have more than two components, and
has been a subject of increasingly intense research interest in recent
years.
It includes the icerule vertex and bond percolation models as special
cases.
The state Potts model consists of a lattice of spins
, which can take different values, and whose Hamiltonian
is

(6.8) 
where the spins take on the values
, and the sum
is over nearest neighbor pairs on sites on a lattice.
For , this is equivalent to the Ising model. The Potts model is
thus a simple extension of the Ising model; however, it has a
richer phase structure, which makes it an important testing ground for
new theories and algorithms in the study of critical phenomena.
Figure 6.2:
The Main Procedure of Potts Model Simulation using Metropolis
Algorithm: One starts with an initial configuration of spins and
repeats these procedures.

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Bryan Carpenter
20040609