Hybrid logic refers to a group of logics lying between modal and first-order logic in which one can refer to individual states of the Kripke structure. In particular, the hybrid logic HL(@, ↓) is an appealing extension of modal logic that allows one to refer to a state by means of the given names and to dynamically create new names for a state. Unfortunately, as for the richer first-order logic...

We study the emergence of giant component in random cluster model on complete graph, which was first studied by Bollobás et al. (1996). give an alternative analysis using a thermodynamic/large deviations approach introduced Biskup (2007) for case percolation. In particular, we compute rate function large size largest connected graph q≥1.