  We study the quantum melting of stripe phases in models with competing short
range and long range interactions decaying with distance as $1/r^{\sigma}$ in
two space dimensions. At zero temperature we find a two step disordering of the
stripe phases with the growth of quantum fluctuations. A quantum critical point
separating a phase with long range positional order from a phase with long
range orientational order is found when $\sigma \leq 4/3$, which includes the
Coulomb interaction case $\sigma=1$. For $\sigma > 4/3$ the transition is first
order, which includes the dipolar case $\sigma=3$. Another quantum critical
point separates the orientationally ordered (nematic) phase from a quantum
disordered phase for any value of $\sigma$. Critical exponents as a function of
$\sigma$ are computed at one loop order in an $\epsilon$ expansion and,
whenever available, compared with known results. For finite temperatures it is
found that for $\sigma \geq 2$ orientational order decays algebraically with
distance until a critical Kosterlitz-Thouless line. Nevertheless, for $\sigma <
2$ it is found that long range orientational order can exist at finite
temperatures until a critical line which terminates at the quantum critical
point at $T=0$. The temperature dependence of the critical line near the
quantum critical point is determined as a function of $\sigma$.
