same values of α as in Fig. 3 in a double logarithmic scale (see caption of Fig. 4 for details). In all the cases we obtain a power law r$_{max}$ ( λ$_{c}$ ) ∼ N − $^{γ}$, with γ = 1 / 4. The results displayed in figures 3 and 4 confirm that the presence of an ESQPT in the environment spectrum is clearly signaled by the qubit decoherence factor. Moreover, the quantity r$_{max}$ behaves in parallel way as the order parameter n$_{t}$ at the ESQPT [11]. Prior to the conclusions, it is worth mentioning that the environmental Hamiltonian Eq. (4) is a particular case of a more generic class of two-level bosonic systems [12], described by H = αn$_{l}$ − (1 − α ) Q ( ω ) l · Q ( ω ) l /N , with Q ( ω ) l = ( s † ˜ l + l $^{†}$s ) ( l ) + ω ( l † ˜ l ) ( l $^{)}$, where the boson s † is a scalar and the boson l † has multipolarity l , as well as the operator Q ( ω ) l depending on an extra parameter ω . As a representative case, we have presented here calculations using the environmental Hamiltonian with l = 0 and ω = 0, characterized by a second order QPT. For l > 1 this wide class of Hamiltonians, that have been extensively used in nuclear and molecular physics, present a richer structure with second order ( ω = 0) and first order ( ω = 0) QPTs. A complete analysis on the influence of the order of the ESQPT in the decoherence process will be given in a future publication. Moreover, as the natural state of a realistic environment is a thermal one —that is, a mixed state in which the environment is in contact with a thermal bath characterized by a temperature T — it will be also interesting to check to which extent the temperature affects this critical behavior. In this paper, we have studied the decoherence induced on a one-qubit system by the in- teraction with a two-level boson environment, which presents both a standard QPT and an ESQPT. Our main finding is that the decoherence is maximal when the system-environment coupling introduces in the environment the energy required to undergo a continuous ESQPT. The decoherence factor displays a critical behavior well described by r$_{max}$ ( λ ), the value of the second local maximum of | r ( t ) | . r$_{max}$ ( λ ) approaches zero for λ → λ$_{c}$ in the thermody- namical limit showing a finite size scaling r$_{max}$ ( λ$_{c}$ ) ∝ N − $^{γ}$, with a critical exponent γ = 1 / 4. Therefore, we conclude that the decoherence induced in a one-qubit system gives a unique signature of an ESQPT in the environment. Finally, let us point out that quantum deco- herence could constitute an important tool to detect critical regions in the energy spectrum of mesoscopic systems; conversely, this knowledge could help to avoid certain environments that are particularly efficient to destroy quantum coherence. Moreover, as the particular Hamiltonian we have studied in this paper has been broadly applied in nuclear structure, molecular physics and, more recently, optical cavity QED, it is feasible to use any of these 8