We propose a theoretical framework based on local gauge symmetries and develop a first-principles-derived effective Hamiltonian to study relaxor ferroelectrics. The approach is applied to PLZT relaxor and i) qualitatively reproduces many of its generic features, such as all the characteristic temperatures inherent to relaxor ferroelectrics and their dependence on the La concentration, ii) yields a rich variety of ferroelectric phases, depending on La content, iii) reveals the existence of non-perfectly ordered regions even in the ferroelectric state, iv) allows, for the first time, to compute the critical exponent γ in a relaxor ferroelectric, and v) clearly elucidates how the relaxor behavior, such as a diffusive phase transition, arises due to the disorder-induced non-trivial interplay between local and global scales. © Copyright EPLA, 2013.