Kuelske C.
The continuous spin random field model:
ferromagnetic ordering in $d\geq 3$
(425K, PS)

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 $\phi^4$ 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 $d\geq 3$.