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In statistical mechanics, a Gibbs measure is a probability measure that relates the probabilities of the various possible states of a system to the energies associated to them. Although the precise definition requires some care (particularly in the case of infinite systems), the main characteristic of a Gibbs measure is that the probability of the system assuming a given state ω with associated energy E(ω) at inverse temperature β is proportional to
Additional recommended knowledge
The definition of a Gibbs random field on a lattice requires some terminology:
A probability measure μ on is a Gibbs measure for a λ-admissible potential Φ if it satisfies the Dobrushin-Lanford-Ruelle (DLR) equations
To help understand the above definitions, here are the corresponding quantities in the important example of the Ising model with nearest-neighbour interactions (coupling constant J) and a magnetic field (h), on :
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Gibbs_measure". A list of authors is available in Wikipedia.|