量子临界性

2011年2月出版的Physics Today杂志上,美国哈佛大学物理学教授Subir Sachdev和德国马克斯.普朗克固体物理研究所Bernhard Keimer所长撰文,就"量子临界性"做了详尽的阐述并指出,在绝对零温度下,由量子涨落导致的相变似乎是一个没有实验意义的、抽象的理论概念,但它却是我们理解众多实验现象的关键.     

Nucleation of solids in solids: ferrites and martensites

When a solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate and the depth of quench. For instance, an infinitesimally slow cooling or a shallow quench results in an equilibrium "ferrite," while a rapid cooling or a deep quench gives rise to a metastable twinned "martensite." In this paper, we arrive at a single formalism which qualitatively describes the transformation to both a ferrite and a martensite. Fundamental to this understanding is our identification of the crucial dynamical role played by nonelastic degrees of freedom in determining the final microstructure of the product solid.     

Three-dimensional elastic compatibility and varieties of twins in martensites

We model a cubic-to-tetragonal martensitic transition by a Ginzburg-Landau free energy in the symmetric strain tensor. We show in three dimensions (3D) that solving the St. Venant compatibility relations for strain, treated as independent field equations, generates three anisotropic long-range potentials between the two order parameter components. These potentials encode 3D discrete symmetries, express the energetics of lattice integrity, and determine 3D textures. Simulation predictions include twins with temperature-varying orientation, helical twins, competing metastable states, and compatibility-induced elastic frustration. Our approach also applies to improper ferroelastics.     

Metamagnetic quantum criticality in metals

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.     

Self-organized criticality in a nutshell

In order to gain insight into the nature of self-organized criticality (SOC), we present a minimal model exhibiting this phenomenon. In this analytically solvable model, the state of the system is fully described by a single-integer variable. The system organizes in its critical state without external tuning. We derive analytically the probability distribution of durations of disturbances propagating through the system. As required by SOC, this distribution is scale invariant and follows a power law over several orders of magnitude. Our solution also reproduces the exponential tail of the distribution due to finite size effects. Moreover, we show that large avalanches are suppressed when stabilizing the system in its critical state. Interestingly, avalanches are affected in a similar way when driving the system away from the critical state. With this model, we have reduced SOC dynamics to a leveling process as described by Ehrenfest's famous flea model.     

Built-up structure criticality

The built-up land represents an important type of an overall landscape. In this paper, the built-up land structure in the largest cities in the Czech Republic and some selected cities in the USA is analysed using the framework of statistical physics. We calculate the variance of the total area and of the count of the built-up land plots contained inside discs of different radii. In both cases, the variance as a function of the disc radius follows a power law with exponents that are comparable through different cities. The study is based on the cadastral data from the Czech Republic and on the building footprints from GIS data in the USA.     

Dynamic criticality in glass-forming liquids

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero-temperature dynamical critical point. To support our proposal, we derive a dynamic field theory for a generic kinetically constrained model, which we expect to describe the dynamics of a supercooled liquid. We study this field theory using the renormalization group (RG). Its long time behavior is dominated by a zero-temperature critical point, which for d>2 belongs to the directed percolation universality class. Molecular dynamics simulations seem to confirm the existence of dynamic scaling behavior consistent with the RG predictions.     

Fluctuations in mean-field self-organized criticality

We present two models that exhibit self-organized criticality at the mean-field level. These can be variously interpreted in epidemiological or chemical reaction terms. By studying the master equation for these models we find, however, that only in one of them does the self-organized critical behavior survive in the face of fluctuations. For this model we show the spectrum of the evolution operator to have spectral collapse, i.e., instead of a gap, as would occur in noncritical behavior, there are eigenvalues that approach zero as an inverse power of system size.     

Semiholographic quantum criticality

We identify the near-critical effective theory (EFT) for a wide class of low-temperature phase transitions found via holography. The EFT is of the semiholographic type and describes both holographic Berezinskii-Kosterlitz-Thouless and second-order transitions with nontrivial scaling. It is a simple generalization of the Ginzburg-Landau-Wilson paradigm to systems with an emergent (or hidden) conformal sector. Having identified the near-critical EFT, we explore its basic phenomenology by computing critical exponents and low-frequency correlators.     

Influence of impurities on phase stability of martensites in titanium

The influence of H, C, N and O impurities on the phase stability of titanium was studied by first principles total energy calculations. The occupation energies of the impurities were estimated to identify their site preferences. All impurities considered prefer to occupy the octahedral site except for H, which tends to occupy the tetrahedral site in the β phase. Electronic structures were analyzed to clarify the intrinsic influence mechanisms of impurity on the stability of martensitic phases. It was found that the density of states around the Fermi energy, which was affected dramatically by impurity, and the bonding interactions between impurity and titanium were connected to the phase stability of Ti. Elastic constants of impurity-containing systems were estimated from curves of energy against strain to evaluate the mechanical stability of these systems. It was shown that the α″ phase can not be stabilized by impurities considered here, while the α′ phase (regardless of the impurities) and H- and C-containing β phase are thermodynamically stable and also satisfy the mechanical stability criteria.     

Evidence for criticality in financial data

The European Physical Journal B - We study the temperature dependencies of the mean sizes of the Cooper pairs in a two-band BCS-type s-wave superconductivity model with coupling cut-off in the...     

Quantum criticality in a double-quantum-dot system

We discuss the realization of the quantum-critical non-Fermi-liquid state, originally discovered within the two-impurity Kondo model, in double-quantum-dot systems. Contrary to common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries and is unstable only to charge transfer between the two dots. We propose an experimental setup where such charge transfer processes are suppressed, allowing a controlled approach to the quantum-critical state. We also discuss transport and scaling properties in the vicinity of the critical point.     

Nature of asymmetry in fluid criticality

By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytical contributions of liquid-gas asymmetry in fluid criticality and showed the validity of "complete scaling" [Fisher, Phys. Rev. Lett. 85, 696 (2000)10.1103/PhysRevLett.85.696; Phys. Rev. E 67, 061506 (2003)10.1103/PhysRevE.67.061506]. We have also developed a method to obtain two scaling-field coefficients, responsible for the two sources of the asymmetry, from mean-field equations of state. Since the asymmetry effects are completely determined by Ising critical exponents, there is no practical need for a special renormalization-group theoretical treatment of asymmetric fluid criticality.     

On self-organised criticality in one dimension

In critical phenomena, many of the characteristic features encountered in higher dimensions such as scaling, data collapse and associated critical exponents are also present in one dimension. Likewise for systems displaying self-organised criticality. We show that the one-dimensional Bak–Tang–Wiesenfeld sandpile model, although trivial, does indeed fall into the general framework of self-organised criticality. We also investigate the Oslo ricepile model, driven by adding slope units at the boundary or in the bulk. We determine the critical exponents by measuring the scaling of the kth moment of the avalanche size probability with system size. The avalanche size exponent depends on the type of drive but the avalanche dimension remains constant.     

Dilution-controlled quantum criticality in rare-earth nickelates

A microscopic model for the diluted spin-mixed compounds (RxY1-x)2BaNiO5 (R=magnetic rare earth) is studied using quantum Monte Carlo simulations. The ordering temperature is shown to be a universal function of the impurity concentration x and the intrinsic Ni-chain correlation length. An effective model for the critical modes is derived. The possibility of a quantum critical point driven by the rare-earth concentration and the existence of a quantum Griffiths phase in the high dilution limit is investigated. Several possible experimental approaches to verify the results are put forward.