Dynamical generation of a gauge symmetry in the double-exchange model

It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and finite-size scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the universality class of the antiferromagnetic RP^(2) model. The fact that one can define a universality class for the antiferromagnetic RP^(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about universality.

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.

Monte Carlo determination of the phase diagram of the double-exchange model

We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features.

Variabilidad de la inactivación microbiana y de la fase de latencia de los microorganismos supervivientes a un proceso de acidificación

A la industria alimentaria se le exigen productos seguros, nutritivos, apetecibles y de uso cómodo y rápido. Aunar todos esos calificativos en un solo alimento es ardua tarea. Valgan dos ejemplos. Un tratamiento conservante intenso, de buenas perspectivas sanitarias, suele conllevar una pérdida de valor nutritivo y unas características sensoriales poco atractivas. El manejo de los alimentos para transformarlos en productos listos pare el consumo implica la asunción de ciertos riesgos microbiológicos, mayores que los asumidos en productos sin manipulación. ¿Cómo responder ante el incremento de riesgos y peligros que se ciernen sobre los “nuevos alimentos”? Una alternativa que ha ganado correligionarios es la microbiología predictiva. Es una herramienta útil, a disposición de cualquier entidad interesada en los alimentos, que predice, mediante modelos matemáticos, el comportamiento microbiano bajo ciertas condiciones. La mayoría de los modelos disponibles predicen valores únicos (a cada valor de la variable independiente le corresponde un único valor de la dependiente); han demostrado su eficacia durante décadas a base de tratamientos sobredimensionados para salvaguardar la calidad microbiológica de los alimentos y predicen una media, sin considerar la variabilidad. Considérese un valor de reducción decimal, D, de 1 minuto. Si el producto contiene 103 ufc/g, un envase de 1 Kg que haya pasado por un tratamiento 6D, contendrá 1 célula viable. Hasta aquí la predicción de un modelo clásico. Ahora piénsese en una producción industrial, miles de envases de 1 Kg/h. ¿Quién puede creerse que en todos ellos habrá 1 microorganismo superviviente? ¿No es más creíble que en unos no quedará ningún viable, en muchos 1, en otros 2, 3 y quizás en los menos 5 ó 6? Los modelos que no consideran la variabilidad microbiana predicen con precisión la tasa de crecimiento pero han fracasado en la predicción de la fase de latencia...

Reconstruction of inclusions in photothermal imaging

Photothermal imaging allows to inspect the structure of composite materials by means of nondestructive tests. The surface of a medium is heated at a number of locations. The resulting temperature field is recorded on the same surface. Thermal waves are strongly damped. Robust schemes are needed to reconstruct the structure of the medium from the decaying time dependent temperature field. The inverse problem is formulated as a weighted optimization problem with a time dependent constraint. The inclusions buried in the medium and their material constants are the design variables. We propose an approximation scheme in two steps. First, Laplace transforms are used to generate an approximate optimization problem with a small number of stationary constraints. Then, we implement a descent strategy alternating topological derivative techniques to reconstruct the geometry of inclusions with gradient methods to identify their material parameters. Numerical simulations assess the effectivity of the technique.

Perturbative Ward identities for Yang-Mills field theory stochastically quantized

%'e compute the divergent part of the three-point vertex function of the non-Abelian Yang-Mills gauge field theory within the stochastic quantization approach to the one-loop order. This calculation allows us to find four renormalization constants which, together with the four previously obtained, verify, to the calculated order, some Ward identities.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

Discontinuous transitions in double-exchange materials

It is shown that the double-exchange Hamiltonian, with weak antiferromagnetic interactions, has a rich variety of first-order transitions between phases with different electronic densities and/or magnetizations. The paramagnetic-ferromagnetic transition moves towards lower temperatures, and becomes discontinuous as the relative strength of the double-exchange mechanism and antiferromagnetic coupling is changed. This trend is consistent with the observed differences between compounds with the same nominal doping, such as La_(2/3)Sr_(1/3)MnO_(3) and La_(2/3)Ca_(1/3)MnO_(3). Our results suggest that, in the low doping regime, a simple magnetic mechanism suffices to explain the main features of the phase diagram.