Well posedness of an integrodifferential kinetic model of Fokker-Planck type for angiogenesis.

Tumor induced angiogenesis processes including the effect of stochastic motion and branching of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the tumor induced ingiogenic factor. The chemotactic force field depends on the flux of blood vessels through the angiogenic factor. We develop an existence and uniqueness theory for this system under natural assumptions on the initial data. The proof combines the construction of fundamental solutions for associated linearized problems with comparison principles, sharp estimates of the velocity integrals and compactness results for this type of kinetic and parabolic operators

Variational mean-field approach to the double-exchange model

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Off-equilibrium fluctuation-dissipation relations in the 3d Ising spin glass in a magnetic field

We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior cannot be completely excluded.

Interplay between double-exchange, superexchange, and Lifshitz localization in doped manganites

Considering the disorder caused in manganites by the substitution Mn→Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the variational mean-field technique. The subtle interplay between double exchange, superexchange, and disorder causes similar effects on the dependence of T_(C) on the percentage of Mn substitution in the cases considered. Yet, in La_(2/3)Ca_(1/3)Mn_(1-y)Ga_(y)O_(3) our results suggest a quantum critical point (QCP) for y ≈ 0.1–0.2, associated to the localization of the electronic states of the conduction band. In the case of La_(x)Ca_(x)Mn_(1-y)Fe_(y)O_(3) (with x = 1/3,3/8) no such QCP is expected.