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Approach to equilibrium of Glauber dynamics in the one phase region (1994)

Martinelli, F. ; Olivieri, E.

Springer

Communications in mathematical physics 161 (1994), S. 487-514

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract We develop a new method, based on renormalization group ideas (block decimation procedure), to prove, under an assumption of strong mixing in a finite cube Λ0, a Logarithmic Sobolev Inequality for the Gibbs state of a discrete spin system. As a consequence we derive the hypercontractivity of the Markov semigroup of the associated Glauber dynamics and the exponential convergence to equilibrium in the uniform norm in all volumes Λ “multiples” of the cube Λ0.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02101930

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