arXiv subjects

Domingos H. U. Marchetti

Publications and source records attributed to Domingos H. U. Marchetti.

21 records · Page 2Linked to original sources

arXiv2000

Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L goes to 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t goes to infinity, to one of the countably infinite equilibrium solutions. The nontrivial equilibrium solution bifurcates from the trivial one. These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature. Gallavotti and Nicolo's conjecture on infinite sequence of ``phases transitions'' is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz-Thouless phases, at least in the hierarchical model we consider.

math-ph↗

arXiv1998

The Falicov-Kimball Model with Long--Range Hopping Matrices

The ground state nature of the Falicov-Kimball model with unconstrained hopping of electrons is investigated. We solve the eigenvalue problem in a pedagogical manner and give a complete account of the ground state energy both as a function of the number of electrons and nuclei and as a function of the total number of particles for any value of interaction U. We also study the energy gap and show the existence of a phase transition characterized by the absence of gap at the half--filled band for U<0. The model in consideration was proposed and solved by Farkasovsky for finite lattices and repulsive on-site interaction U>0. Contrary to his proposal we conveniently scale the hopping matrix to guarantee the existence of the thermodynamic limit. We also solve this model with bipartite unconstrained hopping matrices in order to compare with the Kennedy--Lieb variational analysis.

cond-mat.stat-mech↗

arXiv1993

An alternative to Plemelj-Smithies formulas on infinite determinants

An alternative to Plemelj - Smithies formulas for the p -regularized quantities $d^{(p)}(K)$ and $D^{(p)}(K)$ is presented which generalizes previous expressions with $p=1$ due to Grothendieck and Fredholm. It is also presented global upper bounds for these quantities. In particular we prove that $$ |d^{(p)}(K)| \le e^{κ\n K \n_p^p} $$ holds with $κ= κ(p) \le κ(\infty) = \exp \bigl\{-{1 \over 4(1+ e^{2 π})} \bigr\}$ for $ p\ge 3$ which improves previous estimate yielding $κ(p) = e (2 + \ln(p-1))$.

chao-dyn↗