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 $sigma$.
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