Ti K edge x-ray absorption near-edge structure (XANES) measurements across the pressure induced ferroelectric-paraelectric phase transition in PbTiO_3, a prototypical ferroelectric perovskite, are reported. A quantitative analysis of the XANES allows us to obtain the relative local displacement, directly related to the local electric polarization, of Ti and Pb atoms under pressure. In particular, we found that above the critical pressure, in the so-called cubic-paraelectric phase, the Ti atoms remain locally displaced from their cubic site, indicating that this phase transition has, in a general way, an essential order-disorder component. However, the magnitude of these local displacements is strongly affected by the applied pressure as opposed to what happens as a function of temperature. These conclusions have important consequences in the long standing controversial debate on the interpretation of the ferroelectric phase transition of PbTiO_3 and related family compounds.
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