          \over          \mathscr{Z}^{\mathrm{{ES}}}_{\pmb{p},\pmb{h},G}         }         \sum_{\omega}         B_{\pmb{J}}(\omega)         \Delta(\sigma, \omega)         \times         {\textstyle          \exp         \big(          \beta          \sum_{i\in V} h_i          (\delta_{\sigma_i,0}-\delta_{\sigma_i,-0})         \big)         }         \\[0,0cm]         =         {         C          \over          \mathscr{Z}^{\mathrm{{Potts}}}_{0\beta,\pmb{h},0,V}         }         \sum_{\omega