Anton Bovier, Milos Zahradnik
THE LOW-TEMPERATURE PHASE OF KAC-ISING MODELS
(165K, PS)
ABSTRACT. We analyse the low temperature phase of
ferromagnetic Kac-Ising 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 long-range (almost) continuous
spin system which is suitable for the use of a variant of the Peierls argument.