Limiting behaviors of high dimensional stochastic spin ensembles

  title={Limiting behaviors of high dimensional stochastic spin ensembles},
  author={Yuan Gao and Kay L Kirkpatrick and Jeremy Louis Marzuola and Jonathan C. Mattingly and Katherine A. Newhall},
  journal={Communications in Mathematical Sciences},
Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians are a discrete form of a version of a Dirichlet energy, signifying a relationship to the Harmonic map heat flow equation. The Gibbs distribution, defined with this Hamiltonian, is used in the Metropolis-Hastings (M-H) algorithm to generate dynamics tending towards an equilibrium state. In the limiting situation when the inverse temperature is large, we establish the relationship between the discrete… 

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