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The continuous spin random field model: Ferromagnetic ordering in d>=3

Christof Kuelske
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Abstract

We investigate the Gibbs-measures of ferromagnetically coupled continuous spins in double-well potentials subjected to a random field (our specific example being the $ϕ^4$ theory), showing ferromagnetic ordering in $d\geq 3$ dimensions for weak disorder and large energy barriers. We map the random continuous spin distributions to distributions for an Ising-spin system by means of a single-site coarse-graining method described by local transition kernels. We derive a contour- representation for them with notably positive contour activities and prove their Gibbsianness. This representation is shown to allow for application of the discrete-spin renormalization group developed by Bricmont/Kupiainen implying the result in $d\geq 3$.

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Christof Kuelske. 1998-06-16. The continuous spin random field model: Ferromagnetic ordering in d>=3. https://doi.org/10.1142/s0129055x99000404

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