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1.
非平衡相变的临界标度理论及普适性   总被引:10,自引:0,他引:10  
综述了作者近年来在非平衡相变临界( N P C) 标度理论及普适性研究的进展。主要包括一般 N P C 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 N P C 系统的临界可标度性,导出了一组普适的 N P C 标度关系,由之计算出的4 种 N P C 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。  相似文献   

2.
综述了作者近年来在非平衡相变临界( N P C) 标度理论及普适性研究的进展。主要包括一般 N P C 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 N P C 系统的临界可标度性,导出了一组普适的 N P C 标度关系,由之计算出的4 种 N P C 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。  相似文献   

3.
This paper presents detailed numerical results of the competitive diffusion Lotka-Volterra equation (May-Leonard type). First, we derive the global phase diagrams of attractors in the parameter space including the system size, where transition lines between simple attractors are clearly obtained in accordance with the results of linear stability analysis, but the transition borders become complex when multi-basin structures appear. The complex aspects of the transition borders are studied in the case when the system size decreases. Next, we show the statistical aspects of the turbulence with special attention to the onset of the supercritical Hopf bifurcation. Several characteristic quantities, such as correlation length, correlation time, Lyapunov spectra and Lyapunov dimension, are investigated in detail near the onset of turbulence. Our data show the critical scaling law near the onset only in the restricted parameter domain. However even when the critical indices are not determined accurately, it is shown that the empirical scaling relations are obtained in a wide parameter domain far from the onset point and those scaling indices satisfy several relations. These scaling relations are discussed in comparison with the result derived by the phase reduction method. Lastly, we make a conjecture about the stability of an ecosystem based on the bifurcation diagram: the ecosystem obeying the Lotka-Volterra equation in the case of May-Leonard type is stabilized more as the system size increases.  相似文献   

4.
The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.  相似文献   

5.
Xintian Wu 《Physica A》2007,383(2):209-231
The locally ordered regions (LOR) in the phase transition in disordered systems are studied. There are two parts in this paper. One part is to report our numerical results on the one-dimensional saddle point equation of the Ginzburg-Landau Hamiltonian with random temperature in the presence of an ordering field. The disordered system is modelled as a lattice, on which each cell has a local reduced temperature. The random part of the local reduced temperature is distributed in the Gaussian form. The one-dimensional saddle point equation is solved numerically. The average, the fluctuation and the correlation length of the solution are calculated. The scaling relations for these quantities with the temperature, the ordering field and the disorder strength are derived. The numerical data are fitted with the scaling relations well. Another part is to discuss qualitatively the phase diagram of the finite-range correlated disordered systems. There are two proposed classes for the phase transition in connection with the LOR. One class is described by the percolative scenario, in which the phase transition is inhomogeneous. In the percolative scenario the percolation of the LOR dominates the phase transition. In another class, the phase transition is homogeneous, and can be described by the renormalization group (RG) with replica symmetry breaking (RSB). In the RG with RSB, there is nothing to do with the percolation of LOR. We shall show that these two theories, which seem contradictory, may describe two parts of the whole phase diagram. Whether the phase transition is homogeneous or inhomogeneous depends on the interaction between the LOR. If the interaction between the LOR is strong enough, the phase transition is percolative and inhomogeneous. If the interaction between the LOR is weak, the phase transition is homogeneous. The interaction between the LOR is discussed with the numerical solution on the saddle point equation.  相似文献   

6.
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La2Cu(1-p)(Zn,Mg)(p)O4. Our results are also relevant for disordered interacting boson systems.  相似文献   

7.
We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.  相似文献   

8.
张蕾 《物理学报》2018,67(13):137501-137501
介绍了与斯格明子相关的螺旋磁有序体系的临界行为.首先阐述了连续相变中的临界现象、临界指数、标度律、普适性等概念;随后介绍了磁相变体系中几种临界指数的获得方法,包括直流磁性迭代法、磁熵变法;进而,分析了几类与斯格明子相关的螺旋磁有序体系的临界行为.MnSi是典型的斯格明子材料,临界指数显示其磁性行为符合三重临界行为.MnSi的临界行为揭示:外磁场可以抑制这一体系在零场下的一级相变,使其转变为二级相变,从而在螺旋磁有序、锥形磁有序、顺磁相的三相交汇点形成三重临界点.斯格明子体系FeGe和Cu_2OSeO_3的临界行为符合三维海森伯相互作用,表明它们的磁性行为主要是由近邻的各向同性的自旋耦合作用所决定;而Fe_(1-x)Co_xSi和新发现的斯格明子体系Fe_(1.5-x)Co_xRh_(0.5)MoN的临界行为显示Co掺杂可以有效地调制其中的磁性耦合.对螺旋磁有序体系的临界行为研究表明,尽管这些体系都表现出类似的斯格明子态,但是它们的磁性耦合机制却大不相同,并且其耦合机制可以受到外界手段的调制.最后,根据普适性原理和标度方程,阐述了一种构建磁场诱导相变体系在临界温度附近H-T相图的方法.  相似文献   

9.
We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.  相似文献   

10.
We present Monte Carlo simulations of the isotropic-polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal-isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau's theory of continuous phase transitions.  相似文献   

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