Description

  • set of lattice sites Λ\Lambda each with a set of adjacent sites, (a graph), forming a dd-dimensional lattice
  • spin σk∈{−1,+1}\sigma_k \in \{-1,+1\}, discrete variable for each lattice site k∈Λk \in \Lambda
  • spin configuration σ={σk}k∈Λ\sigma = \{\sigma_k\}_{k \in \Lambda}, assigns a spin value to each lattice site
  • interaction JijJ_{ij} between adjacent i,j∈Λi,j \in \Lambda
  • external magnetic field hjh_j interacting with j∈Λj \in \Lambda
  • energy of σ\sigma, from Hamiltonian function:
    • H(σ)=−∑⟨ij⟩Jijσiσj−μ∑jhjσjH(\sigma) = - \sum_{\langle i j \rangle} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j

Mean field approximation

#incomplete

Notes

  • compare other statistical mechanics models, such as Debye, Einstein, and Potts

See also


References

  1. https://en.wikipedia.org/wiki/Ising_model
  2. https://jeffjar.me/statmech/intro4.html
  3. https://farside.ph.utexas.edu/teaching/329/lectures/node110.html
  4. https://web.mit.edu/ceder/publications/Ising Model.pdf
  5. https://www.cond-mat.de/events/correl15/manuscripts/janis.pdf