Let be a graph representing a lattice (or a rectangular grid). and be the states of spin ``up'' and ``down.'' The Hamiltonian is given by
Attractive spin system. Assuming , the Ising model has the following site update:
Critical temperature. When the temperature is low, spins are aligned, creating a large cluster of aligned states. As the temperature gets higher, the randomness takes over. In the Ising model it is known that this ``phase transition'' occurs at the critical temperature , and that when the graph is a 2-dimensional grid.
Potts Model. Let . Then the Ising model is generalized with the Hamiltonian
© TTU Mathematics