Seminari del Dipartimento
Fisica Matematica Ferromagnetic Spin models with spatially dependent external fields E. Ossami Endo 23-01-2018 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - AULA 311
After Lee-Yang Theorem, we know that the ferromagnetic Ising model on the lattice $mathbb{Z}^d$ with a nonzero and homogeneous external field has no phase transition at any temperature. The problem for inhomogeneous external fields becomes hard since we lose the translational invariance and there is no relation between analytic properties of the pressure and the number of Gibbs states. Recently, it was proved the existence of phase transition at low temperature when the field is given by $h_i=h^*/|i|^{gamma}$, where $iin mathbb{Z}^d$, $h^*>0$ and $gamma>1$. Also, the absence of the phenomenon when $gamma<1$. We present the phase diagram considering the Ising model on Cayley trees with spatially dependent external fields. We discuss the same problem of decaying fields on Dyson models and also the lack of continuity on the $g$-function for these models. The lecture is based on recent papers in collaboration with several authors. |