 96172 Anton Bovier, Milos Zahradnik
 THE LOWTEMPERATURE PHASE OF KACISING MODELS
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May 7, 96

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Abstract. We analyse the low temperature phase of
ferromagnetic KacIsing models in dimensions $d\geq 2$. We show that
if the range of interactions is $\g^{1}$, then two disjoint
translation invariant
Gibbs states exist, if the inverse temperature $\b$ satisfies
$\b 1\geq \g^\k$ where $\k=\frac {d(1\e)}{(2d+2)(d+1)}$, for any
$\e>0$. The prove involves the blocking procedure usual
for Kac models and also a contour
representation for the resulting longrange (almost) continuous
spin system which is suitable for the use of a variant of the Peierls argument.
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