  Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of
materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a
function of length $x$. We show that these are multiscaling, in the sense that
$n^{th}$ order moments of the height fluctuations across any distance $\ell$
scale with a characteristic exponent that depends nonlinearly on the order of
the moment. Having demonstrated this, one rules out a widely held conjecture
that fracture in 2D belongs to the universality class of directed polymers in
random media. In fact, 2D fracture does not belong to any of the known kinetic
roughening models. The presence of multiscaling offers a stringent test for any
theoretical model; we show that a recently introduced model of quasi-static
fracture passes this test.
