Freezing Temperature in Dilute Ising Spin Glasses with Long-Range Interactions

The onset of spin-glass freezing in dilute Ising systems with long-range interactions is investigated with the use of numerical simulations. We show that taking pair correlations explicitly into account results in the renormalization of the interaction matrix and suppression of the density of localized states compared with conventional mean field theory. Application of the theory to the RKKY interaction in the dilute limit raises the question of the appropriate boundary eigenvalue of the effective interaction matrix that separates localized and extended states. We identify the onset of spin-glass freezing with the temperature T _g at which this boundary eigenvalue is equal to one. Numerical simulations reproduces the linear concentration dependence of T _g in the very dilute limit, in agreement with scaling relations, and show a significant improvement over the conventional mean-field theory in the value obtained for the freezing temperature.     

Antifreeze glycoproteins from the antarctic fish Dissostichus mawsoni studied by differential scanning calorimetry (DSC) in combination with nanolitre osmometry

This study investigates in detail the freezing events during cooling of solutions of various size classes of antifreeze glycoproteins. Differential scanning calorimetry and nanolitre osmometry were used to observe ice growth at temperatures within the hysteresis gap between the melting point and non-equilibrium freezing point (hysteresis freezing point) of solutions of the various sized antifreeze glycoproteins (AFGPs). The ice growth within the hysteresis gap is presumably due to both the expression of primary or near primary prism planes and also some growth at the basal plane. The binding of the AFGPs to the ice causes a particular ice crystal morphology. With the smaller AFGPs, substantial microscopic ice growth was observed in the form of a hexagonal bipyramids within the hysteresis gap.     

小尺寸铝纳米团簇的相变行为

采用分子动力学方法模拟了半径从0.3–1.3 nm变化的小尺寸铝纳米团簇的熔化、凝固行为. 基于势能-温度曲线、热容-温度曲线分析, 获得了熔点、凝固点与尺寸的依变关系, 并利用表面能理论、小尺寸效应开展了现象分析.研究表明, 铝团簇原子数小于80时, 熔点和凝固点的尺寸依赖性出现无规律的异常变化; 而大于该原子数, 熔、凝固点则随着团簇尺寸的减小而单调下降; 当原子数为27时, 团簇熔点高于块材熔点近40 K. 同时, 铝纳米团簇呈现出凝固滞后现象, 即凝固点低于熔点. 关键词： 纳米团簇 熔点 凝固点 分子动力学     

Mean-field cage theory for the random close packed state of a metastable hard-sphere glass

In 2005, we developed a mean-field cage theory for the freezing of a stable hard-sphere fluid using the character of a stable hard-sphere fluid, some observations and the mean-configuration approximation [X.Z. Wang, J. Chem. Phys. 122 (2005) 044515]. It was found that near the freezing point, a thermal fluctuation of a cage causes the hard sphere in this cage to exchange positions with one of its nearest neighbors. In this paper, we extend the theory to the random close packed state of a metastable hard-sphere glass. It is found that near the random close packing point, a thermal fluctuation of a cage sets three of the hard spheres in this cage and its nearest cages into the local circulatory motion, resulting in indirect position exchanges among these three hard spheres. We obtain an analytical formula for the random close packing density. The predicted values are in good agreement with the experimental and simulation results for spatial dimensions d=2–7$d=2\text{–}7$.     

壁面静止水滴冻结过程形状变化

低温表面上的液滴冻结时会形成具有尖顶的形状。针对这一现象开展了理论与实验研究,建立了新的动态曲形相界面模型用来模拟水滴冻结过程中的形状变化。模型考虑重力和成核再辉效应的影响,将冻结过程中的冰水相界面近似为球冠形曲面,并在三相点处引入动态生长角和直角关系。对壁面上20μL静止水滴进行了冻结实验,记录水滴三相点高度的演化过程,以此拟合得到了其随时间变化的关联式,基于该关联式求解理论模型,得到了水滴最终冻结形状。模拟结果与实验结果在水滴初始轮廓、成核再辉轮廓和最终冻结轮廓以及冻结时间上均吻合良好。曲面模型的计算结果表明,固液相界面上不同位置处的冻结速率不同;随着相界面向上推移,冻结速率逐渐减小。     

Heterogeneous crystal nucleation: the effect of lattice mismatch

A simple dynamical density functional theory is used to investigate freezing of an undercooled liquid in the presence of a crystalline substrate. We find that the adsorption of the crystalline phase on the substrate, the contact angle, and the height of the nucleation barrier are nonmonotonic functions of the lattice constant of the substrate. We show that the free-growth-limited model of particle-induced freezing by Greer et al. [Acta Mater. 48, 2823 (2000)] is valid for larger nanoparticles and a small anisotropy of the interface free energy. Faceting due to the small size of the foreign particle or a high anisotropy decouples free growth from the critical size of homogeneous nuclei.     

Cluster mode-coupling approach to weak gelation in attractive colloids

Mode-coupling theory (MCT) predicts the arrest of colloids in terms of their volume fraction, and the range and depth of the interparticle attraction. We discuss how the effective values of these parameters evolve under cluster aggregation. We argue that weak gelation in colloids can be idealized as a two-stage ergodicity breaking: first at short scales (approximated by the bare MCT) and then at larger scales (governed by MCT applied to clusters). The competition between the arrest and phase separation is considered in relation to recent experiments. We predict a long-lived "semiergodic" phase of mobile clusters, showing logarithmic relaxation close to the gel line.     

Rigorous results in the mean-field theory of freezing

The mean-field theory of freezing, of which the Kirkwood-Monroe theory is a special case, is formulated in terms of a variational principle which can be derived from a statistical model. New upper and lower bounds on the free energy are found, and used to prove the existence of and to locate a freezing transition. The Kirkwood-Monroe theory is shown to obey a scaling law which implies that the freezing transition has no critical point and that the pressure-temperature phase diagram is a parabola. For a suitable choice of interaction potential, the free energy and density distribution of a crystalline state are calculated with very small error. The variational principle yields an integral equation found previously by van Kampen. This equation is derived rigorously, and shown to admit solutions of any chosen periodicity. The equation is transformed into a nonlinear integral equation of the Hammerstein type, and some standard uniqueness theorems applied. The equation is also transformed into a set of linear equations closely resembling the Kirkwood-Salsburg equations. Many unsolved problems are raised.     

Experimental test of the dynamical coulomb blockade theory for short coherent conductors

We observed the recently predicted quantum suppression of dynamical Coulomb blockade on short coherent conductors by measuring the conductance of a quantum point contact embedded in a tunable on-chip circuit. Taking advantage of the circuit modularity we measured most parameters used by the theory. This allowed us to perform a reliable and quantitative experimental test of the theory. Dynamical Coulomb blockade corrections, probed up to the second conductance plateau of the quantum point contact, are found to be accurately normalized by the same Fano factor as quantum shot noise, in excellent agreement with the theoretical predictions.     

Close-packed floating clusters: granular hydrodynamics beyond the freezing point?

Monodisperse granular flows often develop regions with hexagonal close packing of particles. We investigate this effect in a system of inelastic hard spheres driven from below by a "thermal" plate. Molecular dynamics simulations show, in a wide range of parameters, a close-packed cluster supported by a low-density region. Surprisingly, the steady-state density profile, including the close-packed cluster part, is well described by a variant of Navier-Stokes granular hydrodynamics (NSGH). We suggest a simple explanation for the success of NSGH beyond the freezing point.     

Clarification of the bootstrap percolation paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.     

Bubble-nucleation rates for radiatively induced first-order phase transitions

We present a consistent calculation of bubble-nucleation rates in theories of two scalar fields. Our approach is based on the notion of a coarse-grained free energy that incorporates the effects of fluctuations with momenta above a given scale k. We establish the reliability of the method for a variety of two-scalar models and confirm the conclusions of previous studies in one-field theories: Langer's theory of homogeneous nucleation is applicable as long as the expansion around the semi-classical saddle point associated with tunnelling is convergent. This expansion breaks down when the exponential suppression of the rate by the saddle-point action becomes comparable to the pre-exponential factor associated with fluctuations around the saddle point. We reconfirm that Langer's theory is not applicable to the case of weakly first-order phase transitions. We also find that the same is true in general for radiatively induced first-order phase transitions. We discuss the relevance of our results for the electroweak phase transition and the metastability bound on the Higgs-boson mass.     

Suppression of spin-orbit scattering in strongly disordered gold nanojunctions

We discovered that spin-orbit scattering in strongly disordered gold nanojunctions is strongly suppressed relative to that in weakly disordered gold thin films. This property is unusual because in weakly disordered films spin-orbit scattering increases with disorder. Granularity and freezing of spin-orbit scattering inside the grains explains the suppression of spin-orbit scattering. We propose a generalized Elliot-Yafet relation that applies to a strongly disordered granular regime.     

Refining the risk of freezing mortality for antarctic terrestrial microarthropods

In studies of three common, freezing susceptible, Antarctic microarthropods, the springtail Cryptopygus antarcticus and the mites Alaskozetes antarcticus and Halozetes belgicae, we report (i) the consequences on cold tolerance of cooling in contact with water, and (ii) the risk of freezing when held at temperatures above the typical freezing point (measured using standard techniques) for up to 12 h. The springtail showed no change in SCP distribution when in contact with freezing water while, in contrast, the mites showed clear shifts towards decreased cold tolerance, in addition to death of c. 33% of individuals during the freezing of the water. The springtail showed a bimodal SCP distribution, with the population divided into "high"(typically -8 to -12 degree C) and "low" (typically below -20 degree C) groups. Some animals held at temperatures above these values froze, over a timescale between minutes and several hours. These results highlight the danger of equating standard cold tolerance measures with mortality risk under more realistic water and thermal regimes.     

Universal behavior of shear viscosity near the freezing point

The dynamics of liquids above the freezing point is studied. It is demonstrated that the available experimental data on shear viscosity of simple liquids can be described in the framework of the so-called weak crystallization theory. The theory predicts that, in the main approximation, shear viscosity is proportional to the (T/T _*−1)^−3/2, where T _* is the temperature close to the freezing temperature. This prediction is in good agreement with experimental data for many substances.     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

Finite Size Corrections to the Parisi Overlap Function in the GREM

We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model in two situations where replica symmetry is broken in the thermodynamic limit. Our calculations do not use replicas, but shed some light on what the replica method should give for finite size corrections. In the gradual freezing situation, which is known to exhibit full replica symmetry breaking, we show that the finite size corrections lead to a modification of the simple relations between the sample averages of the overlaps \( Y_k \) between k configurations predicted by replica theory. This can be interpreted as fluctuations in the replica block size with a negative variance. The mechanism is similar to the one we found recently in the random energy model in Derrida and Mottishaw (J Stat Mech 2015(1): P01021, 2015). We also consider a simultaneous freezing situation, which is known to exhibit one step replica symmetry breaking. We show that finite size corrections lead to full replica symmetry breaking and give a more complete derivation of the results presented in Derrida and Mottishaw (Europhys Lett 115(4): 40005, 2016) for the directed polymer on a tree.     

Surface freezing on patterned substrates

We show that the structure of a substrate pattern drastically influences the nature of surface freezing. By using phenomenological theory and computer simulations of a hard sphere fluid next to a substrate formed by a periodic array of fixed spheres, we find that a pattern which is commensurate with the bulk crystal induces complete surface freezing through a cascade of layering transitions. A rhombic pattern, on the other hand, either generates a crystalline sheet which is unstable as a bulk phase or prohibits surface freezing completely.     

Aesthetic fields—Null theory II

We have again studied a null theory within the complex aesthetic field theory. This time we required that the spatially inverted origin point data represent the imaginary part of the complex origin point data. This was not the case in our previous studies of the null aesthetic field theory. However, this procedure did not lead to effects not previously observed as far as we could tell. Adding an additional term to the origin point data that presented the null character of the theory also did not lead to new effects. We also investigated a real null theory that led to constant fields. This theory was then made complex by a procedure discussed in the early part of the paper. We found that the resulting complex theory remained trivial nevertheless. Again, we found that it was not necessary for the theory to be null to find confluence type solutions.     

Towards a description of the Kondo effect using time-dependent density-functional theory

We demonstrate that the zero-temperature conductance of the Anderson model can be calculated within the Landauer formalism combined with static density-functional theory. The proposed approximate functional is based on finite-temperature density-functional theory and yields the exact Kohn-Sham potential at the particle-hole symmetric point. Furthermore, in the limit of zero temperature it correctly exhibits a derivative discontinuity which is shown to be essential to reproduce the conductance plateau. On the other hand, at the Kondo temperature the exact Kohn-Sham conductance overestimates the real one by an order of magnitude. To understand the failure of density-functional theory, we resort to its time-dependent version and conclude that the suppression of the Kondo resonance must be attributed to dynamical exchange-correlation corrections.