Microcanonical Approach to the Simulation of First-Order Phase Transitions

A generalization of the microcanonical ensemble suggests a simple strategy for the simulation of first order phase transitions. At variance with flat-histogram methods, there is no iterative parameters optimization, nor long waits for tunneling between the ordered and the disordered phases. We test the method in the standard benchmark: the Q-states Potts model (Q=10 in 2 dimensions and Q=4 in 3 dimensions), where we develop a cluster algorithm. We obtain accurate results for systems with more than one million of spins, outperforming flat-histogram methods that handle up to tens of thousands of spins.Comment: 4 pages, 3 postscript figure

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both Lattice field-theories and of models of Statistical Mechanics, identities verified by exact mean-values such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well known and sensitive tests of thermalization bias as well as checks of pseudo random number generators. We point out that they can be further exploited as "control variates" to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the two dimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.Comment: 10 pages, 2 tables. References updated and typos correcte

Lattice-Spin Mechanism in Colossal Magnetoresistant Manganites

We present a single-orbital double-exchange model, coupled with cooperative phonons (the so called breathing-modes of the oxygen octahedra in manganites). The model is studied with Monte Carlo simulations. For a finite range of doping and coupling constants, a first-order Metal-Insulator phase transition is found, that coincides with the Paramagnetic-Ferromagnetic phase transition. The insulating state is due to the self-trapping of every carrier within an oxygen octahedron distortion.Comment: 4 pages, 5 figures, ReVTeX macro, accepted for publication in PR

Optimized Monte Carlo Method for glasses

A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm is shown to thermalize well below the Mode Coupling temperature and to outperform other optimized Monte Carlo methods. Using the algorithm, we obtain finite size effects in the specific heat. This effect points to the existence of a large correlation length measurable in equal time correlation functions.Comment: Proceedings of "X International workshop on Disordered Systems" held in Molveno (Italy), March 200

Finite size effects in the specific heat of glass-formers

We report clear finite size effects in the specific heat and in the relaxation times of a model glass former at temperatures considerably smaller than the Mode Coupling transition. A crucial ingredient to reach this result is a new Monte Carlo algorithm which allows us to reduce the relaxation time by two order of magnitudes. These effects signal the existence of a large correlation length in static quantities.Comment: Proceeding of "3rd International Workshop on Complex Systems". Sendai (Japan). To appear on AIP Conference serie

Rejuvenation and Memory in model Spin Glasses in 3 and 4 dimensions

We numerically study aging for the Edwards-Anderson Model in 3 and 4 dimensions using different temperature-change protocols. In D=3, time scales a thousand times larger than in previous work are reached with the SUE machine. Deviations from cumulative aging are observed in the non monotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the D=3$site-diluted ferromagnetic Ising model (without chaos). However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.Comment: Extended protocols. Accepted in Phys. Rev. B. 10 postscript figure

On the critical behavior of the specific heat in glass-formers

We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the Finite Size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.Comment: Version to be published in Phys. Rev.

Vibrations in glasses and Euclidean Random Matrix theory

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), the Euclidean random matrix theory provide a single and fairly simple theoretical framework to their explanation.Comment: 11 pages, 7 postscript figures, Proceedings of Statphys 2

Vibrational spectra in glasses

The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key ingredient which strongly affects the vibrational spectra of those systems. We present a resummation scheme for a perturbative expansion in the inverse particle density, allowing an accurate analytical computation of the dynamical structure factor within the range of densities encountered in real systems.Comment: Talk given at the '8th International Workshop on Disordered Systems' Andalo, Trento, 12-15 March 200