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Gibbs measureIn 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 knowledgeFormal definitionThe definition of a Gibbs random field on a lattice requires some terminology:
A probability measure μ on is a Gibbs measure for a λadmissible potential Φ if it satisfies the DobrushinLanfordRuelle (DLR) equations
An exampleTo help understand the above definitions, here are the corresponding quantities in the important example of the Ising model with nearestneighbour interactions (coupling constant J) and a magnetic field (h), on :
References

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. 