electric fields, which distort the orientation of dipoles. While the precise consequence of the random field is not all clear [@Sherrington2014; @Kleemann2015], such distracting effect on dipoles appears to lead to a strongly modified phase transition with diffused and smeared peak, in sharp contrast to that of normal ferroelectrics [@Pirc2007; @PMNeffHami2015].

To model such a system and account for the moderate phase transition, we need a function that properly describes the dielectric constant versus temperature. Here, we propose to use the slightly modified well known quadratic relation $\frac{\varepsilon_{A}}{\varepsilon^{\prime}}-1=\frac{\left(T-T_{A}\right)^{2}}{2\delta^{2}}$ proposed by Bokov *et al* [@Bokov2006a] to relate relaxor’s permittivity to temperature [@Smolenskii1970; @Kirillov1973] for dipoles above the average potential well (also see Eq. (\[eq:square-law\]) ). This equation can be rearranged to give the following expression $$\begin{aligned}
w_{2}\left(T\right)= & \frac{1}{1+\left|\frac{T-T_{O}}{\theta}\right|^{\gamma}},\label{eq:w2t}\end{aligned}$$ where $\gamma$ is a critical exponent, $T_{o}$ is associated with the peak position of the moderate phase transition, $\theta$ and $\gamma$ are parameters describing the peak. We note that such choice of $w_{2}\left(T\right)$ also agree with the analysis recently given by Uchino [@Uchino2014]. Combining Eqs. (\[eq:total-susceptibility\]) and (\[eq:w2t\]), we obtain the following equation to fit lead-based relaxors, $$\begin{aligned}
\chi\left(T\right)= & \frac{\chi_{1}}{1+\left|\frac{T-T_{O}}{\theta}\right|^{\gamma}}P\left(E_{b},T\right)+\chi_{2}\left[1-P\left(E_{b},T\right)\right],\label{eq:PZN}\end{aligned}$$ where $E_{b}$, $\chi_{1}$, $\chi_{2}$, $T_{o}$, $\theta$, and $\gamma$ are fitting parameters. 