arXiv subjects
Publications and source records attributed to Carlos Vasquez.
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
We review some results on the effect of a specific type of quenched disorder on well known O(m)-vector models in three dimension. Evidences of changes of criticality in both systems, when confined in aerogel pores, are briefly referenced. The 3DXY model (m=2) represents the universality class to which the λ-transition of bulk superfluid $^4$He belongs. Experiments report changes of critical exponents for this transition, when superfluid $^4$He is confined in aerogels. Numerical results of the 3DXY model, confined in aerogel-like structures, are in agreement with experiments. Both results seem to contradict Harris criterion: being the specific heat exponent negative for the pure system, changes must be explained in terms of the extended criterion due to Weinrib and Halperin, which requires disorder to be long-range correlated (LRC) at all scales. Aerogels are fractal through some decades only, and present crossovers to homogeneous regimes at finite scales, so the violation to Harris criterion persists. The apparent violation has been explained in terms of hidden LRC subsets within aerogels $[$Phys. Rev. Lett., 2003, {\bf 90}, 170602$]$. On the other hand, experiments on the liquid-vapor (LV) transition of $^4$He and N$_2$ confined in aerogels, also showed changes in critical-point exponents. Being the LV critical-point in the O(1) universality class, criticality may be affected by both, short-range correlated (SRC) and LRC subsets ofdisorder. Simulations of the 3DIS in DLCA aerogels can corroborate experimental results. Experiments and simulations both suggest a shift in critical exponents to values closer to the SRC instead of those of the LRC fixed point.
The influence of correlated impurities on the critical behaviour of the 3D Ising model is studied using Monte Carlo simulations. Spins are confined into the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behaviour of this magnetic system. Finite size scaling is used to estimate critical couplings and exponents. Long-range correlated disorder does not affect critical behavior. Asymptotic exponents differ from those of the pure 3D Ising model (3DIS), but it is impossible, with our precision, to distinguish them from the randomly diluted Ising model (RDIS).