COEXISTENCE OF INFINITE (ASTERISK)-CLUSTERS .2. ISING PERCOLATION IN 2 DIMENSIONS

We show a strong type of conditionally mixing property for the Gibbs states of d-dimensional Ising model when the temperature is above the critical one. By using this property, we show that there is always coexistence of infinite (+ *)- and (- *)-clusters when beta is smaller than beta(c) and h = 0 in two dimensions. It is also possible to show that this coexistence region extends to some non-zero external field case, i.e., for every beta < beta(c), there exists some h(c)(beta) > 0 such that Absolute value of h < h(c)(beta) implies the coexistence of infinite (*)-clusters with respect to the Gibbs state for (beta, h).