  Compounds containing magnetic subsystems representing simple model spin
systems with weak magnetic coupling constants are ideal candidates to test
theoretical predictions for the generic behavior close to quantum phase
transitions. We present measurements of the thermal expansion and
magnetostriction of the spin-1/2-chain compound copper pyrazine dinitrate
Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$. Of particular interest is the low-temperature
thermal expansion close to the saturation field $H_c \simeq 13.9 \mathrm{T}$,
which defines a quantum phase transition from the gapless Luttinger liquid
state to the fully saturated state with a finite excitation gap. We observe a
sign change of the thermal expansion for the different ground states, and at
the quantum critical point $H_c$ the low-temperature expansion approaches a
$1/\sqrt{T}$ divergence. Thus, our data agree very well with the expected
quantum critical behaviour.
