Harris Criterion Research Articles

PFNA治疗老年骨质疏松性股骨粗隆间骨折

目的：探讨防旋型股骨近端髓内钉(Proximal Femoral Nail Anti-Rotation, PFNA)治疗老年骨质疏松性股骨粗隆间骨折的疗效。方法：自2010年11月~2013年11月应用PFNA治疗34例老年骨质疏松性股骨粗隆间骨折的患者。骨折按照AO分型，A1型10例A2型13例A3型11例。统计手术时间，术中出血量，术后进行骨质疏松的治疗及术后骨折愈合时间；随访6~11个月。结果：34例患者平均手术时间65分钟，术中出血量平均160 ml，所有病例随访6~11个月骨折均愈合，平均愈合时间7.5个月。无断钉、切割、髋内翻等现象。根据Harris评分：优25例，良7例，可2例，优良率：94.1%。结论：PFNA治疗老年骨质疏松性股骨粗隆间骨折，创伤小，固定牢固，操作方便，有利于患者骨折早期愈合和肢体功能恢复。 Objective: To observe the therapeutic effect of senile osteoporotic femoral intertrochanteric fractures treated with proximal femoral nail anti-rotation (PFNA). Method: From 2010 to 2013, 34 cases (11 males, 23 females) of senile osteoporosis femoral intertrochanteric fractures were treated with PFNA, who aged from 62 to 87. According to the classification of AO, there were 10 cases of A1, 13 cases of A2, 11 cases of A3. Operative time, volume of blood loss and the condition of fracture union were observed with the follow-up of 6 - 11 months. Results: mean operating time was 65 minutes, mean intraoperative bleeding volume was 160 ml, cases were followed up from 6 months to 11 months, and mean healing time was 7.5 months. According to the Harris criterion for evaluation, the effects were excellent in 25 cases, good in 7 cases and fair in 2 cases, the excellent and good rate was 94.1%. Conclusion: The treatment of senile osteoporosis femoral intertrochanteric fracture with PFNA is less traumatic, fixed firmly and operated simply, in favor of fracture healing and function recover.

Image Matching Based on Improved Harris Criterion Algorithm

We illustrate the development of an application for cultivar classification of leaf images based on the extraction of the network of its main veins that runs on mobile devices like smart phones or tablets. Such mobile devices can be docked to farming robots in order to support the farming process. Our application uses an efficient Gabor filter-based tracing algorithm which is able to perform a robust network extraction. The results are used as input data for the classification with a support vector machine. In order to demonstrate the advantageous behavior and the robustness of this method, we perform an evaluation on a test set consisting of 150 light transmitted images of different vine leaves.

Phase diagram and critical behavior of the random ferromagnet Ga1−xMnxN

Molecular beam epitaxy has been employed to obtain Ga1-xMnxN films with x up to 10% and Curie temperatures T_C up to 13 K. The magnitudes of T_C and their dependence on x, T_C(x) ~ x^m, where m = 2.2 +/- 0.2 are quantitatively described by a tight binding model of superexchange interactions and Monte Carlo simulations of T_C. The critical behavior of this dilute magnetic insulator shows strong deviations from the magnetically clean case (x = 1), in particular, (i) an apparent breakdown of the Harris criterion; (ii) a non-monotonic crossover in the values of the susceptibility critical exponent gamma_eff between the high temperature and critical regimes, and (iii) a smearing of the critical region, which can be explained either by the Griffiths effects or by macroscopic inhomogeneities in the spin distribution with a variance Delta x = (0.2 +/- 0.1)%.

Superfluid transition in a correlated defect network

Motivated by recent experiments on possible supersolid behavior of $^4$He solids at low temperature, we consider a model of superfluidity in a defected solid containing a system spaning network of correlated linear dislocations, or planar grain boundaries. Using arguments based on the Harris criterion, as well as numerical simulations, we find that such correlated quenched disorder shifts the familiar superfluid lambda transition to a new disordered universality class in which the correlation length exponent $\nu\ge 1$. This results in the temperature-derivates for the superfluid density, $d\rho_{\rm s}/dT$, and for the heat capacity, $dc/dT$, remaining finite at the transition $T_{\rm c}$, and thus a less singular transition, profoundly different from the usual lambda transition.

Multiple quantum criticality in a two-dimensional superconductor

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Critical behavior in Sr-doped manganites La0.6Ca0.4−xSrxMnO3

The critical behavior of La0.6Ca0.4−xSrxMnO3 (x=0, 0.2 and 0.4) compounds has been investigated based on the data of static magnetic measurements in the vicinity of its critical temperature TC. Through various techniques such as modified Arrott plot, Kouvel–Fisher method and critical isotherm analysis, the estimated critical exponents are found to be (β=0.267, γ=0.992, δ=4.896 at TC=268.12), (β=0.501, γ=1.045, δ=2.992 at TC=344.37) and (β=0.386, γ=1.293, δ=4.88 at TC=371.02), for x=0, 0.2 and 0.4; close to tricritical mean field, mean field and 3D-Heisenberg model values, respectively. The reliability of the critical exponents values was confirmed by the Widom scaling relation and the universal scaling hypothesis. Following the Harris criterion, we deduced that the disorder in our case is relevant, which can be the cause of the change in the universality class. Moreover, the local exponent n was studied in terms of the field dependence of the magnetic entropy change. It has been noted that n evolves with field in the entire studied temperature range for all samples. The invalidity of the mean field model for x=0 and 0.4 contents was confirmed at the peak temperature. Far above the transition temperature, the Curie–Weiss law is well satisfied. The differences observed in the n values below the transition are mentioned. Furthermore, unlike the modified Arrott or Kouvel–Fischer methods, the performed analysis is shown to be useful to examine critical exponents and their effects in mixed phases materials.

Nonequilibrium Relaxation Study of Effect of Randomness on Critical Universality Classes of Ferromagnetic Phase Transitions

The ferromagnetic critical exponents are estimated along the phase boundary for the gauge glass model in three dimensions. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents. Together with the previously obtained results for the ± J Ising model in two and three dimensions, universality classes are examined for these disordered models. The result reveals a direct numerical confirmation of the Harris criterion for typical models with positive, zero and negative values of α 0 , the exponent for the specific heat in the regular case. In addition, we show a nonuniversal behavior of the dynamical exponent z with respect to the randomness for these models irrespective of α 0 .

Random pinning model with finite range correlations: Disorder relevant regime

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.

Effect of calcium deficiency on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.8Ca0.2MnO3 oxides

The critical behavior associated with the magnetic phase transition has been investigated by magnetization isotherms in La0.8Ca0.2MnO3 and La0.8Ca0.1□0.1MnO3 (□ is the calcium deficiency). The critical exponents are estimated by various techniques such as the Modified Arrott plot, Kouvel–Fisher plot and critical isotherm technique. The critical exponents values for La0.8Ca0.2MnO3 are very close to those found out by the 3D-Ising model (β=0.328, γ=1.180, and δ=4.826 at an average TC=181.676K). Moreover, the estimated critical exponents of La0.8Ca0.1□0.1MnO3 are consistent with the prediction of the 3D-Heisenberg model (β=0.357, γ=1.167, and δ=4.802 at an average TC=178.182K). We noted that the critical exponents γ are almost similar to the value of the mean-field theory which can be explained by the existence of a long-range dipole–dipole interaction. Following the Harris criterion, we deduced that the disorder in our case is relevant, which can be the cause of the change in the universality class.

Determination of the critical exponents for absorbing phase transitions in the conserved lattice gas model in three dimensions

The critical exponents were measured for absorbing phase transitions in the conserved lattice gas (CLG) model on a simple cubic lattice. The correlation-length exponent calculated from the dynamic exponent obtained by finite-size scaling and from the mean spreading distance was consistently found to be ν(⊥)=0.631±0.02, which yields a positive specific heat exponent α=2-dν(⊥) on a pure system. The pure fixed point should, thus, be unstable if the Harris criterion established in equilibrium systems is applicable to the nonequilibrium absorbing phase transitions of the CLG model. However, this prediction is in contradiction with recent simulation results.

Sharp critical behavior for pinning models in a random correlated environment

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e., without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion (Harris, 1974) [21].

Influence of quenched disorder on absorbing phase transitions in the conserved lattice gas model

Motivated by the Harris criterion, the absorbing phase transitions of the conserved lattice gas (CLG) model were studied on lattices with a quenched disorder, i.e., on infinite percolation networks, in two and three dimensions. The Harris criterion suggests that, in a magnetic system, the pure fixed point will be unstable if the specific-heat exponent is positive. For the CLG model, the specific-heat exponent α calculated by the hyperscaling relation α=2-dν, where ν is the spatial correlation length exponent in d dimensions, will be positive in two dimensions if the value of ν obtained earlier by Lübeck and Heger is employed. On the other hand, it will be close to 0 if the more recent value by Lee and Lee is used and it is positive in three dimensions with the available value of ν. Extensive numerical simulations showed that, when the concentration of disordered sites is less than the critical concentration, the critical exponents were similar to those on a regular lattice both in two and three dimensions. When the concentration of disordered sites becomes critical, the density of active particles showed nonuniversal power-law behavior for all particle densities considered in both dimensions. These results were in contrast to the results for the diluted contact process. The cause of such a nonuniversal behavior was addressed.

Observation of mixed anisotropy in the critical susceptibility of an ultrathin magnetic film

Measurements of the magnetic susceptibility of Fe/W(110) films with thickness in the range of 1.6 to 2.4 ML Fe, show that in addition to the large response along the easy axis associated with the Curie transition, there is a much smaller, paramagnetic hard axis response that is not consistent with the 2D anisotropic Heisenberg model used to describe homogeneous in-plane ferromagnets with uniaxial anisotropy. The shape, amplitude, and peak temperature of the hard axis susceptibility, as well as its dependence upon layer completion close to 2.0 ML, indicate that inhomogeneities in the films create a system of mixed anisotropy. A likely candidate for inhomogeneities that are magnetically relevant in the critical region are the closed lines of step edges associated with the incomplete layers. According to the Harris criterion, the existence of magnetically relevant inhomogeneities may alter the critical properties of the films from those of a 2D Ising model. Experiments in the recent literature are discussed in this context.

Monte Carlo simulations of the site-diluted three-dimensional XY model

We present extensive Monte Carlo simulations of the classical XY model in three dimensions on a simple cubic lattice with periodic boundary conditions subject to quenched, random site dilution. By using a hybrid algorithm and finite-size scaling techniques we estimate the transition temperatures and the critical exponents associated with the diluted system. Our results for the critical exponents and universal cumulants are, within statistical errors, the same as for the zero dilution case and are independent of the amount of dilution, in agreement with the Harris criterion. The initial reduction of the critical temperature with dilution is also evaluated and compared to recent experimental results.

Monte Carlo analysis of the critical properties of the two-dimensional randomly bond-diluted Ising model via Wang–Landau algorithm

The influence of random bond-dilution on the critical properties of the two-dimensional Ising model on a square lattice with periodic boundary conditions is presented using the Monte Carlo process with Wang–Landau sampling. The lattice linear size is L = 20 – 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution, namely, q = 0.05 , 0.1 , 0.2 , 0.3 , 0.4 ; the respective percolation limit for the square lattice is q c P E R C = 0.5 . Its pure version ( q = 0 ) has a second-order phase transition with vanishing specific heat critical exponent, an example of inapplicability of the Harris criterion. The main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents. We have also looked at the probability distribution of the susceptibility, pseudocritical temperature and specific heat for assessing self-averaging. The study is carried out in the appropriately restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the critical exponents are estimated; the specific heat exponent vanishes, the correlation-length exponent ν is equal to one and the critical exponents’ ratio ( γ / ν ) retains its pure-Ising-model value, thus supporting the strong universality hypothesis.

Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J' in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J'. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.

Treatment of intertrochanteric fractures with proximal femur nail antirotation

Objective To summarize the experiences in treatment of intertochanteric fractures with proximal femur nail antirotation (PFNA). Methods A retrospective study was done on 136 patients with intertrochanteric fractures treated with PFNA from March 2006 to September 2008. Postoperative reduction quality, long-term radiographic results and function of hip were evaluated separately. All the patients had closed fractures. The operation involved orthopedic traction bed, C-arm image intensifier,closed reduction or limited open reduction and locking technique. Results All patients were followed up for 10-18 months (average 14.5 months), which showed fracture healing in all patients. According to Harris criterion, the function of the hip joint obtained excellence in 129 patients ( 94.9% ). Conclusion PFNA has advantages of simple procedure, minimal invasion, firm fixation and early functional exercises and is an effective method for treatment of intertrochanteric fractures. Key words: Femur; Hip fractures; Fracture fixation,internal; Proximal femur nail antirotation

Critical behavior of diluted magnetic semiconductors: Apparent violation and eventual restoration of the Harris criterion for all regimes of disorder

Using large-scale Monte Carlo calculations, we consider strongly disordered Heisenberg models on a cubic lattice with missing sites (as in diluted magnetic semiconductors such as ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$). For disorder ranging from weak to strong levels of dilution, we identify Curie temperatures and calculate the critical exponents $\ensuremath{\nu}$, $\ensuremath{\gamma}$, $\ensuremath{\eta}$, and $\ensuremath{\beta}$; we find, per the Harris criterion, good agreement with critical indices of the pure Heisenberg model where there is no disorder component. Moreover, we find that thermodynamic quantities (e.g., the second moment of the magnetization per spin) self-average at the ferromagnetic transition temperature with relative fluctuations tending to zero with increasing system size. We directly calculate effective critical exponents for $T&gt;{T}_{c}$, yielding values which may differ significantly from the critical indices for the pure system, especially in the presence of strong disorder. Ultimately, the difference is only apparent, and eventually disappears when $T$ is very close to ${T}_{c}$.

Marginal relevance of disorder for pinning models

AbstractThe effect of disorder on pinning and wetting models has attracted much attention in theoretical physics. In particular, it has been predicted on the basis of the Harris criterion that disorder is relevant (annealed and quenched models have different critical points and critical exponents) if the return probability exponent α, a positive number that characterizes the model, is larger than ½. Weak disorder has been predicted to be irrelevant (i.e., coinciding critical points and exponents) if α &lt; ½. Recent mathematical work has put these predictions on firm ground. In renormalization group terms, the case α = ½ is a marginal case, and there is no agreement in the literature as to whether one should expect disorder relevance or irrelevance at marginality. The question is also particularly intriguing because the case α = ½ includes the classical models of two‐dimensional wetting of a rough substrate, of pinning of directed polymers on a defect line in dimension (3 + 1) or (1 + 1), and of pinning of an heteropolymer by a point potential in three‐dimensional space. Here we prove disorder relevance both for the general α = ½ pinning model and for the hierarchical pinning model proposed by Derrida, Hakim, and Vannimenus, in the sense that we prove a shift of the quenched critical point with respect to the annealed one. In both cases we work with Gaussian disorder and we show that the shift is at least of order exp(−1/β4) for β small, if β2 is the disorder variance. © 2009 Wiley Periodicals, Inc.

Fractional Moment Bounds and Disorder Relevance for Pinning Models

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For \alpha 1, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is known to be smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered by Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and remains open.