[en] Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent η is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local LC structure. The β-function is calculated exactly and found non-analytic, with a critical exponent ω 2, in agreement with the conformal field theory prediction of Calabrese et al