Ising model

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Ising Model

The Ising model is commonly defined over an ordered lattice. Each site of the lattice can adopt two states: either UP (S=+1) or DOWN (S=-1).

The energy of the system is the sum of pair interactions between nearest neighbors.

where indicates that the sum is done over nearest neighbors, and indicates the state of the i-th site.

is called the Coupling constant.

to be continued:

  • Ising in 1-d (exact solution)
  • Usual lattices in 2d: Critical behavior
  • Lattices in 3-d
  • Ferromagnetic and antiferromagnetic couplings
  • Frustration, etc
  • Simulation procedures
  • Theoretical methods