Three-dimensional Ising model in the fixed-magnetization ensemble: a Monte Carlo study

We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of microscopic spin-up and spin-down probabilities in a given configuration of neighbors. In the thermodynamic limit, the relation between this field and the magnetization reduces to the canonical relation M(h). However, for finite systems, the relation is different. We establish a close connection between this relation and the probability distribution of the magnetization of a finite-size system in the canonical ensemble.Comment: 8 pages, 2 Postscript figures, uses RevTe

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Physical tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations.Comment: 16 pages, Post Script file, HU-TFT-94-

Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test di erent mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.Comment: submitted to Physical Review B (2004

Finite size scaling in the 2D XY-model and generalized universality

In recent works (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2D XY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size --in the range of the lattice sizes studied-- below the Kosterlitz-Thoules temperature. However, the shape of these distributions does depend on the temperature, contrarily to the BHP's claim. This behavior is successfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.Comment: 7 pages, 5 figures. Submitted to Phys. Rev. Lett. Details of changes: 1. We emphasized in the abstract the range of validity of our results. 2. In the last paragraph the temperature dependence of the PDF was slightly re-formulate

Strong rejuvenation in a chiral-glass superconductor

The glassy paramagnetic Meissner phase of a Bi$_2$Sr$_2$CaCu$_2$O$_x$ superconductor ($x$ = 8.18) is investigated by squid magnetometry, using ``dc-memory'' experiments employed earlier to study spin glasses. The temperature dependence of the zero-field-cooled and thermo-remanent magnetization is recorded on re-heating after specific cooling protocols, in which single or multiple halts are performed at constant temperatures. The 'spin' states equilibrated during the halts are retrieved on re-heating. The observed memory and rejuvenation effects are similar to those observed in Heisenberg-like spin glasses.Comment: REVTeX 4 style; 5 pages, 5 figure

Universal Magnetic Fluctuations with a Field Induced Length Scale

We calculate the probability density function for the order parameter fluctuations in the low temperature phase of the 2D-XY model of magnetism near the line of critical points. A finite correlation length, \xi, is introduced with a small magnetic field, h, and an accurate expression for \xi(h) is developed by treating non-linear contributions to the field energy using a Hartree approximation. We find analytically a series of universal non-Gaussian distributions with a finite size scaling form and present a Gumbel-like function that gives the PDF to an excellent approximation. We propose the Gumbel exponent, a(h), as an indirect measure of the length scale of correlations in a wide range of complex systems.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.

Untersuchungen zur Optimierung eines chemischen Prozesses für die Herstellung von YBa₂Cu₃O₇₋ₓ-Schichten

Untersuchungen zur Optimierung eines chemischen Prozesses für die Herstellung von YBa2Cu3O7-x-Schichten Der oxidische Supraleiter YBa2Cu3O7-x wurde über verschiedene naßchemische Verfahren hergestellt, wobei die Acetylacetonate und Alkoholate von Yttrium, Barium und Kupfer sowie ein Heterometall-oxo-alkoholat eingesetzt wurden. Die thermische Zersetzung der metallorganischen Precursoren wurde unter dem Aspekt, den Prozeß zu optimieren, thermogravimetrisch und durch die Charakterisierung der Zersetzungsprodukte untersucht. Die gasförmigen Produkte konnten mit Hilfe der TGA-FTIR-Kopplung kontinuierlich erfaßt werden, die festen hingegen diskontinuierlich mittels Röntgenpulverdiffraktometrie und FT-IR-Spektroskopie charakterisiert. Am Beispiel des Acetylacetonat-Precursors wurde der Einfluß der Atmosphäre auf die thermische Zersetzung umfassend dargestellt. Unter inerten Bedingungen entstand elementares Kupfer und Bariumcarbonat sowie geringe Anteile an kristallinem Y2O3 und BaY2O4. Die Pyrolyse an Luft führte zur supraleitenden Phase. Die kritischen Temperaturen der YBa2Cu3O7-x-Pulver von ca. 90 K wurden durch Magnetisierungsmessungen bestimmt. Über das optimierte Verfahren konnten c-Achsen-texturierte YBa2Cu3O7-x-Schichten auf (100)-orientierten SrTiO3-Substraten hergestellt werden. Die supraleitenden Schichten zeigten bei Tc,onset = 90 K eine sprungartige Widerstandsänderung mit einem DTc von 7 K