Analysis Of Critical Behavior Research Articles

Comment on “Renormalization-group picture of the Lifshitz critical behavior”

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B 67, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not give an ultraviolet finite renormalized theory, is plagued by inconsistencies, misses the existence of a nontrivial anisotropy exponent $\ensuremath{\theta}\ensuremath{\ne}1/2,$ and therefore yields incorrect hyperscaling relations. His $\ensuremath{\epsilon}$-expansion results to order ${\ensuremath{\epsilon}}^{2}$ for the critical exponents of m-axial Lifshitz points are incorrect in both the anisotropic $(0<m<d)$ and isotropic $(m=d)$ cases. The inherent inconsistencies and the lack of a sound basis of the approach makes its results unacceptable even if they are interpreted in the sense of approximations.

Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points

We investigate the critical behavior that d-dimensional systems with short-range forces and an n-component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in an m-dimensional isotropic subspace of R d . Utilizing dimensional regularization and minimal subtraction of poles in d=4+ m 2 −ϵ dimensions, we carry out a two-loop renormalization-group (RG) analysis of the field-theory models representing the corresponding universality classes. This gives the beta function β u ( u) to third order, and the required renormalization factors as well as the associated RG exponent functions to second order, in u. The coefficients of these series are reduced to m-dependent expressions involving single integrals, which for general (not necessarily integer) values of m∈(0,8) can be computed numerically, and for special values of m analytically. The ϵ expansions of the critical exponents η l2 , η l4 , ν l2 , ν l4 , the wave-vector exponent β q , and the correction-to-scaling exponent are obtained to order ϵ 2. These are used to estimate their values for d=3. The obtained series expansions are shown to encompass both isotropic limits m=0 and m= d.

Analysis of the Critical Behavior of the Metal–Insulator Transition by Variation of the Compensation in Neutron Transmutation Doped 74Ge–70Ge Crystals

Analysis of the Critical Behavior of the Metal–Insulator Transition by Variation of the Compensation in Neutron Transmutation Doped 74Ge–70Ge Crystals

固有値問題の摂動展開による釣合経路上の臨界点予測手法

The exact prediction of critical points on the equilibrium path is desired in the numerical analysis of critical behavior of a structure. A new strategy for predicting the critical point is proposed here by applying the incremental perturbation method to eigenvalue problem. The variations in eigenvalues are evaluated by solving the ordered perturbation equations successively. The perturbation equations can be solved by applying the generalized inverse. The solution of algebraic equation, which sets the each eigenvalue to zero with respect to incremental parameter, gives the step length to the critical point. Two typical examples for critical behavior show that the strategy proposed here can predict the critical point of structure model with high accuracy.

Critical behavior of a smectic-Ato nematic phase transition imbedded in a random network of voids

Department of Physics, Kent State University, Kent, Ohio 44240~Received 13 August 1997!We present the results of a systematic ac calorimetric study on the smectic-A to nematic ~Sm-A–N! phasetransition for the alkylcyanobiphenyl liquid crystals, 8CB and 9CB, imbedded in the randomly interconnectedvoids of Millipore cellulose membranes. The confining void size ranged from 5 to 0.025mm, which, althoughlarge, introduces substantial changes compared to the bulk behavior. The heat capacity peak at the Sm-A–Ntransition temperature changes from sharp and prominent to broad and small with increased confinement.Concomitant with the heat capacity peak shape change, critical behavior analysis reveals that the randomconfinement drives the heat capacity critical exponent from its bulk value towards zero, approaching thethree-dimensionalXY universality class value prediction of 20.007. This change in the critical exponent isliquid-crystal material and voids size dependent, and is equivalent to what occurs with increasing nematicrange that weakens the coupling between smectic and nematic order parameters. The Millipore confinementdoes not alter the nematic range; it is the randomness it introduces that changes the nature of the coupling. Inaddition, but in a manner not fully consistent with finite size effects, transition temperatures are shifted downfrom bulk and the transition enthalpy is suppressed. Supporting results are found in a study of binary mixturesof 9CB and 10CB. @S1063-651X~98!02504-5#PACS number~s!: 64.70.Md, 61.30.2v, 65.20.1wINTRODUCTION

Subtleties in data analysis related to the size of critical region

We comment on the analysis of the critical behavior of a layered driven diffusive system recently done by Achahbar and Marro. We discuss why we believe their method of taking the thermodynamic limit and determining the order-parameter exponent β leads to unreliable estimates.

Analysis of multifragmentation in a Boltzmann-Langevin approach

By using the Boltzmann-Langevin equation, which incorporates dynamical fluctuations beyond usual transport theories, we simulate the $^{40}\mathrm{Ca}$${+}^{40}$Ca reaction system at different beam energies 20, 60, and 90 MeV/nucleon for different impact parameters. Dynamical fluctuations become larger and larger with increasing bombarding energy and the system can reach densities corresponding to the unstable region of the nuclear matter equation of state at energies above 60 MeV/nucleon. By coupling the Boltzmann-Langevin equation with a coalescence model in the late stages of the reaction, we obtain the distribution of the intermediate mass fragments in each event. From the correlation analysis of these fragments, we recover some trends of recent multifragmentation data. A critical behavior analysis is also provided.

Light-Scattering and TEM Analyses of Virtual Upper Critical Solution Temperature Behavior in PCL/SAN Blends

The presence of a virtual upper critical solution temperature (UCST) of PCL/SAN blends was found at lower temperatures. Time-resolved light scattering under V v and H v optical alignments was used in order to distinguish two competitive processes-crystallization and liquid-liquid phase separation of blends quenched below the melting point. The occurrence of a closed miscibility window can be explained in terms of an equation of state theory

Stability behaviour of semi-rigid sway frames

Due to the inelastic behaviour of beam-to-column connections, the stability behaviour of semi-rigid steel frames is affected not only by the loading and unloading characteristics of connections at the critical points, but also by their prior load history up to these points. Thus, the analysis of inelastic critical and post-critical behaviour of semi-rigid frames becomes very complicated, when compared with that of the usual pinned or rigid frames. This paper utilizes a method developed by the authors to examine precisely how the stability behaviour of semi-rigid frames is influenced by factors such as modelling of connections, load conditions, geometrical imperfections, and the load history caused by cyclic wind load. Based on these results, the validity of the effective length factor as applied to the design of semi-rigid frames is discussed.

Light scattering analysis of upper critical solution temperature behavior in a poly(vinylidene fluoride)/poly(methyl methacrylate) blend

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTLight scattering analysis of upper critical solution temperature behavior in a poly(vinylidene fluoride)/poly(methyl methacrylate) blendHideaki Tomura, Hiromu Saito, and Takashi InoueCite this: Macromolecules 1992, 25, 5, 1611–1614Publication Date (Print):March 1, 1992Publication History Published online1 May 2002Published inissue 1 March 1992https://doi.org/10.1021/ma00031a038RIGHTS & PERMISSIONSArticle Views415Altmetric-Citations62LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (446 KB) Get e-Alerts Get e-Alerts

Analysis of critical behavior of semi-rigid frames with or without load history in connections

Due to the inelastic behavior of beam-to-column connections, the critical behavior of semi-rigid frames is affected not only by the loading and unloading characteristics of connections at the critical points, but also by their load history up to these points. Thus, the stability analysis of frames of this type becomes very complicated, compared with pinned or rigid frames. Herein, we shall present a refined method which can accurately analyze the inelastic, critical behavior of semirigid frames, i.e. bifurcation and limit load instability. This method can also take into account the load history caused by cyclic loading. Using the proposed method, the rectangular semi-rigid frames wilh or without the load history due to cyclic wind load are precisely analyzed to examine their inelastic critical behavior.

Investigation of the Smectic C* - Smectic A Phase Transition in Electric Field

Abstract A sharp maximum of the soft mode strength has been observed at the chiral smectic C* - smectic A phase transition using on optical detection method. The soft mode peak has been used as an indicator of the phase trantision in the absence of external electric field. Electric field broadens the maximum and shifts it towards higher temperatures. Analysis of the soft mode critical behaviour shows that the dc field does not affect the phase transition temperature.

Analysis of the critical behaviour of curved regions in equilibrium shapes of In crystals

Analysis of the critical behaviour of curved regions in equilibrium shapes of In crystals

Buckling and sensitivity estimates for ring-stiffened cylinders under external pressure

An analysis of critical and post-critical behaviour of cylinders under external pressure with widely spaced stiffeners is presented. The ring-stiffeners are treated as discrete elements and their torsional plus bending stiffness are taken into account and their effect on the most relevant results are evaluated. Solutions are presented to show the effect of shell and ring geometric parameters on the critical loads and imperfection-sensitivity. Buckling loads are estimated and compared with available test results and recommended design curves.

Analysis of electric susceptibility data and critical behaviour in the uniaxial ferromagnet LiHoF4using correlated-effective-field theory

Measurements of the electric susceptibility (which is orthogonal to the magnetic susceptibility) in LiHoF4 show a sharp cusp at Tc that cannot be explained by simple mean-field theory. Correlated-effective-field (CEF) theory is applied to this system and is found to provide an excellent fit to the data over a wide range of temperatures. In addition the critical behaviour of LiHoF4 is re-examined by the application of the authors' CEF model to the precise order-parameter data of Griffin and co-workers (1980). Although the authors' CEF model ultimately shows classical critical behaviour, over the temperature range of the data it yields a fit of quality equivalent to that obtained by Griffin and co-workers using renormalisation-group theory. Hence the experiments of Griffin and co-workers do not unequivocally establish a marginal dimensionality of three for LiHoF4.

Analysis of critical and post-critical behaviour of non-linear dynamical systems by the normal form method, Part II: Divergence and flutter

The normal form method (NFM) presented in Part I [1] is applied to the analysis of systems near two basic bifurcation conditions: divergence and flutter. The “reduced systems”, and the normalizing transformation, obtained by means of a computer routine implementing the normalization formulae of Part I, are utilized to determine (a) the stability of the bifurcating singular point, (b) the local equilibrium paths associated with divergence bifurcation, and (c) the amplitude and frequency (or, more generally, the waveform) of post-flutter oscillations.

Analysis of critical and post-critical behaviour of non-linear dynamical systems by the normal form method, Part I: Normalization formulae

A method, based on normal form theory, is presented to study the dynamical behaviour of a system in the neighbourhood of a nearly critical equilibrium state associated with a bifurcation condition. Explicit formulae for the normalization procedure are derived. These formulae can be numerically programmed, avoiding usual complicated algebraic calculations and making the method effectively applicable for n-dimensional systems. Rather general bifurcations can be included: e.g., non-linear flutter (Hopf bifurcation), divergence and internal resonance.

Critical behaviour of transport coefficients at a structural-ferromagnetic transition. I. Electrical resistivity of TbZn

The electrical resistivity rho and its temperature derivative d rho /dT of two TbZn monocrystals have been studied over a large temperature range encompassing the Curie temperature (Tc approximately 199.56K) and the spin reorientation temperature (Tr approximately 61.9K). Particular emphasis is put on the critical behaviour analysis. A detailed study shows that a scaling law behaviour characterised by a finite but fairly small critical exponent cannot be experimentally distinguished from a logarithmic dependence above Tc. The cross-over temperature to the mean field behaviour is also pointed out. Outside the critical region, the anomalously large d rho /dT values observed over most of the ferromagnetic range are explained using a mean field model. Finally, the critical behaviour of d rho /dT near Tr is analysed, and the resemblance to the anomaly observed in the specific heat is pointed out.