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Jacopo De Simoi

Publications and source records attributed to Jacopo De Simoi.

21 records · Page 2Linked to original sources
arXiv2008

Potts models on hierarchical lattices and Renormalization Group dynamics

We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also consider models with an applied external magnetic field and multiple-spin interactions. We use recent results regarding iteration of rational maps in several complex variables to show that, for some class of hierarchical lattices, Lee-Yang and Fisher zeros belong to the unstable set of the renormalization map.

cond-mat.stat-mech↗
arXiv2008

Potts models on hierarchical lattices and Renormalization Group dynamics II: examples and numerical results

We obtain the exact renormalization map and plots of Lee-Yang and Fisher zeros distributions for Potts models on a number of hierarchical lattices: the diamond hierarchical lattice, a lattice we call spider web, the Sierpinski gasket and cylinders. Such models are only examples among the ones we can study in the general framework of hierarchical lattices, developed in a previous paper.

cond-mat.stat-mech↗
arXiv2008

Stability and instability results in a model of Fermi acceleration

We consider the static wall approximation to the dynamics of a particle bouncing on a periodically oscillating infinitely heavy plate while subject to a potential force. We assume the case of a potential given by a power of the particle's height and sinusoidal motions of the plate. We find that for powers smaller than 1 the set of escaping orbits has full Hausdorff dimension for all motions and obtain existence of elliptic island of period 2 for arbitrarily high energies for a full-measure set of motions. Moreover we obtain conditions on the potential to ensure that the total (Lebesgue) measure of elliptic islands of period 2 is either finite or infinite.

math.DS↗