The rough phase of random percolation
Ferdinando Gliozzi
Abstract
Three-dimensional percolation
can be thought as a gauge theory in
disguise.
Although the gauge group is trivial, being composed of only one
element,
the percolating phase captures the
salient properties of the
confining
vacuum of ordinary gauge theories. Owing
to the triviality of
the gauge
group there is no character expansion, however it is possible to
define
another kind of expansion showing confinement near the saturation
limit at
p=1, where the
where the
whole flux is concentrated. As in
any gauge theory these surfaces
undergo a
roughening transition. The rough phase is characterised
by the
occurrence of universal shape effects in
to those
observed in fluid interfaces in magnetic systems.