$ac$ electric field closely, leading $w_{1}\left(T\right)$ to its maximum; and (ii) at higher temperature, thermal motions of these dipoles hamper their ability to follow the *ac* electric field, leading to smaller $w_{1}\left(T\right)$. We will discuss this equation further in Sec. \[subsec:Discussion\]. With one more parameter ($b$), this function may be taken as an extension to the Langevin function.

                  1 GHz   10 GHz   100 GHz   1000 GHz
  -------------- ------- -------- --------- ----------
   $\theta$ (K)   579.6   762.6    1128.4      2158
    $\chi_{1}$    406.5   312.6     209.3      99.9
    $\chi_{2}$    73.1     63.5     56.2       57.9
       $b$        10.2     9.9       9.5       7.7

  : Fitting parameters of numerically simulated Ba(Zr$_{0.5}$,Ti$_{0.5}$)O$_{3}$ susceptibility at various frequency [@Wang2016] using Eq. (\[eq:BZT-frequency\]). \[tab:Fitting-parameters-of-BZT\]

![Analysis of fitting parameters versus probing frequency. (a) $\chi_{1}$vs $\log\left(f\right)$; (b) $w_{1}\left(T\right)$. \[fig:w1T\]](Fig3_ab){width="8cm"}

We use Eq. (\[eq:BZT-frequency\]) to fit BZT’s susceptibility versus temperature at different frequency and show the results in Fig. \[fig:Fitting-BZT-frequency\]. Since $E_{b}$ is a material parameter, we use the same value ($E_{b}=159.1$ K) obtained by fitting the static susceptibility (cf. Fig. \[fig:Fitting-susceptibility-of\]). In Fig. \[fig:Fitting-BZT-frequency\], the numerical results are obtained from molecular dynamics simulations reported in Ref. [@Wang2016]. As the figure shows, satisfactory fittings are achieved for frequencies between 1 and 1000 GHz. Table \[tab:Fitting-parameters-of-BZT\] shows all the parameters. 