Consider independent long range percolation on Z, where edges of length n are open with probability pn. We show that if lim supnâ†’âˆž pn > 0, then there exists an integer N such that PN (0â†”âˆž) > 0, whereâ€¦ (More)

At first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable, which is conjugate to an order parameter for the transition. This result isâ€¦ (More)

At first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable, which is conjugate to an order parameter for the transition. This result isâ€¦ (More)

We report about two new rigorous results on the nonanalytic properties of thermodynamic potentials at first-order phase transition. For lattice models (d>or=2) with arbitrary finite state space,â€¦ (More)

We study the analyticity properties of the free energy fÎ³(m) of the Kac model at points of first order phase transition, in the van der Waals limit Î³ â†˜ 0. We show that there exists an inverseâ€¦ (More)

We report about two new rigorous results on the non-analytic properties of thermodynamic potentials at first order phase transition. The first one is valid for lattice models (d â‰¥ 2) with arbitraryâ€¦ (More)

Consider independent long range percolation on Z2, where horizontal and vertical edges of length n are open with probability pn. We show that if lim supnâ†’âˆž pn > 0, then there exists an integer N suchâ€¦ (More)