2011
DOI: 10.1063/1.3559129
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A cluster expansion approach to renormalization group transformations

Abstract: The renormalization group (RG) approach is largely responsible for the considerable success which has been achieved in developing a quantitative theory of phase transitions. This work treats the rigorous definition of the RG map for classical Ising-type lattice systems in the infinite volume limit at high temperature. A cluster expansion is used to justify the existence of the partial derivatives of the renormalized interaction with respect to the original interaction. This expansion is derived from the formal… Show more

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Cited by 2 publications
(1 citation statement)
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“…Using cluster expansion techniques as in [22], we show that the Hypothesis also guarantees the existence of the partial derivatives of the RG transformation (Theorem 4.6). By a more careful analysis, we will then show that the partial derivative decays sub-exponentially as the distance between the set in the original lattice and the set in the image lattice gets large.…”
Section: Introductionmentioning
confidence: 89%
“…Using cluster expansion techniques as in [22], we show that the Hypothesis also guarantees the existence of the partial derivatives of the RG transformation (Theorem 4.6). By a more careful analysis, we will then show that the partial derivative decays sub-exponentially as the distance between the set in the original lattice and the set in the image lattice gets large.…”
Section: Introductionmentioning
confidence: 89%