![]() ![]() In particular, we start with the empty torus and are interested in the first time when the torus is fully covered by disks. We are interested in the metastable behaviour of the system at low temperature when the chemical potential is supercritical. Consequently, the interaction between the particles is attractive. The particles are viewed as points carrying disks and the energy of a particle configuration is equal to minus the volume of the total overlap of the disks. This talk concerns the metastable behaviour of the Widom-Rowlinson model on a two-dimensional torus subject to a stochastic dynamics in which particles are randomly created and annihilated as if the outside of the torus were an infinite reservoir with a given chemical potential.Metastability for the Widom-Rowlinson model On the energy landscape of an elastic manifold in random potential This is based on joint work with Michael Aizenman The proof is based on a delicate study of intersection properties of a non-Markovian random walk appearing in the random current representation of the model. #Paradigm Speaker Serial Numbers freeIn this talk, we show that any continuum phi^4 theory constructed from Reflection Positive lattice φ 4 or Ising models is inevitably free in dimension 4. While non-triviality results in d4 were obtained in famous papers by Glimm, Jaffe, Aizenman, Frohlich and others, the crucial case of dimension 4 remained open. ![]() a field with non-zero Ursell functions, is at the heart of Euclidean (quantum) field theory.
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