Domingos H. U. Marchetti

Griffiths' singularities in diluted ising models on the Cayley tree

The Griffiths singularities are fully exhibited for a class of diluted ferromagnetic Ising models defined on the Cayley tree (Bethe lattice). For the deterministic model the Lee-Yang circle theorem is explicitly proven for the magnetization at the origin and it is shown that, in the thermodynamic limit, the Lee-Yang singularities become dense in the entire unit circle for the whole ferromagnetic phase. Smoothness (infinite differentiability) of the quenched magnetizationm at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder. From our analysis we also conclude that the existence of metastable states is impossible for the random models under consideration.

The Kosterlitz-Thouless phase transition in two-dimensional hierarchical Coulomb gases

AbstractA hierarchical version of two-dimensional lattice Coulomb gases is investigated. Forβ>βc=8π there is a locally stable line of fixed points for the renormalization group (“block charges”) transformations. For

The 1/N-expansion as a perturbation about the mean field theory: A one-dimensional fermi model

\beta > \bar \beta _c (\beta _c \leqslant \bar \beta _c \leqslant \tfrac{3}{2}\pi \beta _c )

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

, these fixed points are globally stable. As a consequence we show that there is no screening of external charges for any activity if

Phase Transitions in Layered Systems

\beta > \bar \beta _c

Layered Systems at the Mean Field Critical Temperature

. Atβca supercritical bifurcation takes place and we investigate the behavior of the model forβ≲βcto show a weak form of screening.