Determination Of Critical Exponents Research Articles

Influence of nanocrystallization on the magnetocaloric properties of Ni-based amorphous alloys: Determination of critical exponents in multiphase systems

Traditionally the study of the magnetocaloric effect (MCE) in amorphous and nanocrystalline alloys has been focused on Fe and rare earth based compositions. However, they present problems that hinder their application such as the high price of rare earths or the necessary addition of a large fraction of non-magnetic elements in Fe-based alloys in order to tune their response to temperatures close to room temperature. Alternatively, Ni-based amorphous alloys have the Curie temperature (TC) well below room temperature and with a good glass forming ability. For these alloys, Fe addition provides a good tool to tune TC close to room temperature. In this work, the magnetocaloric properties of Ni82−xFexSi2B16 (x = 8, 12, 13.2, 16) have been studied in the amorphous and nanocrystalline state. Besides compositional dependence of MCE in this series, a detailed analysis of the critical exponents of the magnetic transition of both amorphous and nanocrystalline alloys has been performed using the magnetic field dependence of MCE. Results were compared with those derived from the Kouvel-Fisher method, requiring a deconvolution of the different magnetization contributions in the Kouvel-Fisher case for nanocrystalline alloys.

Scheme independence and the exact renormalization group

We compute critical exponents in a Z 2 symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion. At leading order all our results are cutoff independent, while at next-to-leading order they are not, and the determination of critical exponents becomes ambiguous. We discuss the possible ways in which this scheme ambiguity might be resolved.

Determination of critical exponents from the multifragmentation of gold nuclei.

Using reverse kinematics, we have studied the breakup of 1.0[ital A] GeV gold nuclei incident on a carbon target. The detector system permitted exclusive event reconstruction of nearly all charged reaction products. The moments of the resulting charged fragment distribution provide strong evidence that nuclear matter possesses a critical point observable in finite nuclei. We have determined values for the critical exponents [gamma], [beta], and [tau]. These values are close to those for liquid-gas systems and clearly different than those for 3D percolation and the liquid-gas mean field limit.

A master equation investigation of coagulation reactions: Sol‐gel transition

AbstractThe kinetics of irreversible coagulation phenomena in spatially homogeneous systems is formulated in terms of a multivariate stochastic process. The latter is governed by a master equation for the joint probability distribution of the numbers of reacting species. An efficient numerical algorithm is used to simulate the complete time evolution of the stochastic process. The method is illustrated by simulating the coagulation reaction with configuration‐dependent reaction kernels, Kij = (ij)ω, for clusters of mass i and j with 1/2 < ω ⩽ 1, which are designed to model gelation phenomena. It is demonstrated that the stochastic simulation allows the determination of critical exponents and the gel point directly from the master equation. The results are compared to predictions of the rate equation approach to the sol‐gel transition.

Truncation errors in the Monte Carlo renormalization group: A comparative study.

An explanation is given for the impressive success Swendsen has had in the determination of critical exponents using his method of truncation in the space of operators. A by-product is a way to further improve his numbers and estimate residual truncation errors.

Reliability of low-energy electron diffraction for studies of surface order-disorder phenomena.

It is shown that a determination of critical exponents in surface phase transformations based on a kinematic analysis of LEED peak intensities is subject to errors caused by multiple scattering that are large enough to prevent a clear assignment to a known universality class. The multiple-scattering contribution arises from short-range flucutations and has its maximum value at the transition temperature. The specific-heat exponent of the surface phase can be measured directly from the variation of the integral-order-beam intensity with temperature that is caused by the multiple scattering.

Gravity Effects near the Gas-Liquid Critical Point

The "linear-model" parametric equation of state of Schofield, Litster, and Ho is used to analyze the effect of gravity near the gas-liquid critical point of a fluid. Detailed results are presented on the density distribution as a function of height, the constant-volume specific heat, and the low-frequency sound velocity, for arbitrary points in the ($\ensuremath{\rho}, T$) plane near the critical point. The influence of gravity on the determination of critical exponents is also considered. It is concluded that even for the thinnest practical samples, gravity corrections may have a significant effect on the exponents. The present theory permits gravity corrections to be made in a self-consistent way, with high accuracy.

Determination of critical exponents from measurements of binary vapor-liquid equilibrium in the neighborhood of the critical line

The shape of the coexistence curve for a binary vapor-liquid equilibria along several isotherms has been found to be described by ( y − x) = c( P c mix − P) β , where y and x are the concentrations of the more volatile component in the vapor and liquid phases, respectively; P c mix is the critical pressure of the isotherm; P is the pressure; and c is a proportionality constant. A value of β = 1 3 ± 0.05 describes the data of the methaneethane and methane-propane systems from the critical point of methane to 23°K higher for pressures within 10 psi of the critical pressure of the isotherm. The proportionality constant c appears to have a generalized linear temperature dependence applicable to both systems. The behavior of the heavier component from 1.35°K above the more volatile (methane) component critical temperature to at least 9°K higher is mathematically represented by the same type of exponential function for a much wider pressure range of approximately 300 psi.