$ by the formula $$H_{\Lambda|\eta}(\sigma)= \sum_{(\gamma_x ,\tilde{\gamma}_y) \in e_{\Lambda}(\sigma|\eta)} U( \gamma_x , \tilde{\gamma}_y )$$ where $$\label{wru}     U(\gamma_x,\tilde{\gamma}_y) := \left\{ \begin{array}{ll} +\infty &\text{if }\gamma \neq \tilde{\gamma}\text{ and }\|x-y\|_\infty \leq r\\ 0 &\text{otherwise}\end{array}\right.$$ and $$e_{\Lambda}(\sigma|\eta) := \{ (\gamma_x ,\tilde{\gamma}_y) \in \langle \sigma \cdot \eta_{\Lambda^c \times G} \rangle^0 : x \in \Lambda \}