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We study the quantum melting of stripe phases in models with competing shortrange and long range interactions decaying with distance as $1/r^{\sigma}$ intwo space dimensions. At zero temperature we find a two step disordering of thestripe phases with the growth of quantum fluctuations. A quantum critical pointseparating a phase with long range positional order from a phase with longrange orientational order is found when $\sigma \leq 4/3$, which includes theCoulomb interaction case $\sigma=1$. For $\sigma > 4/3$ the transition is firstorder, which includes the dipolar case $\sigma=3$. Another quantum criticalpoint separates the orientationally ordered (nematic) phase from a quantumdisordered 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 isfound that for $\sigma \geq 2$ orientational order decays algebraically withdistance until a critical Kosterlitz-Thouless line. Nevertheless, for $\sigma <2$ it is found that long range orientational order can exist at finitetemperatures until a critical line which terminates at the quantum criticalpoint at $T=0$. The temperature dependence of the critical line near thequantum critical point is determined as a function of $\sigma$.

Quantum and thermal melting of stripe forming systems with competing long ranged interactions