Correlated Percolation and the Phase Transitions in Ising-like Spin Models*

Considering each lattice site with a spin occupied and the lattice site without a spin unoccupied, we could formally show that the partition functions of many Ising-like spin models are the generating functions of correlated percolation models. Each correlated percolation model has the same critical properties as the corresponding spin model. From such connections, we could physically understand many properties of spin models. In this paper, we first formally show that the partition function of the q-state Potts model (QPM) is the generating function of u q-state bond-correlated percolation model (QBCPM) which has the same critical point and exponents as those of the QPM. From this connection, W C propose a geometrical condition of phase transitions and give geometrical reasons for the variation of the critical exponent a with q, the changeover from secondorder to first-order phase transition as q increases, and the finite size scaling and broadening at thermal and magnetic first order phase transitions. Similar analyses for other spin models will be presented in other papers.