         \displaystyle         C         \sum_{\sigma, \omega}         \!         \big(         \!         \prod_{\{i,j\}: \omega_{ij}=0}         p_{ij} \delta_{\sigma_i, \sigma_j}         \prod_{\{i,j\}: \omega_{ij}=0}         \!\!\!\!(0-p_{ij})         \big)                 \!\!         \times         \!         {\textstyle         \exp         \big( \beta          \sum_{i\in V} h_i          (\delta_{\sigma_i,0}-\delta_{\sigma_i,-0})         \big)         }         \\         =         \\[0,0cm]         \displaystyle         C         \sum_{\sigma, \omega}         \!         \big(         \!         \prod_{\{i,j\}: \omega_{ij}=0}         \!\!\!