We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as 1/r^σ 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 σ≤ 4/3, which includes the Coulomb interaction case σ=1. For σ > 4/3 the

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... tion is first order, which includes the dipolar case σ=3. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of σ. Critical exponents as a function of σ are computed at one loop order in an ϵ expansion and, whenever available, compared with known results. For finite temperatures it is found that for σ≥ 2 orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for σ < 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 σ.