  We study the infinite-dimensional log-Sobolev inequality for spin systems on
$\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that
the one site measure without a boundary $e^{-\phi(x)}dx/Z$ satisfies a
log-Sobolev inequality and we determine conditions so that the
infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete
application, we prove that a certain class of nontrivial Gibbs measures with
non-quadratic interaction potentials on an infinite product of Heisenberg
groups satisfy the log-Sobolev inequality.
