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Ultracold polar molecules, in highly anisotropic traps and interacting via arepulsive dipolar potential, may form one-dimensional chains at high densities.According to classical theory, at low temperatures there exists a criticalvalue of the density at which a second order phase transition from a linear toa zigzag chain occurs. We study the effect of thermal and quantum fluctuationson these self-organized structures using classical and quantum Monte Carlomethods, by means of which we evaluate the pair correlation function and thestatic structure factor. Depending on the parameters, these functions exhibitproperties typical of a crystalline or of a liquid system. We compare thethermal and the quantum results, identifying analogies and differences.Finally, we discuss experimental parameter regimes where the effects of quantumfluctuations on the linear - zigzag transition can be observed.

Thermal and quantum fluctuations in chains of ultracold polar molecules