Classical Critical Behavior Research Articles

Conduction Mechanism Switching from Coulomb Blockade to Classical Critical Percolation Behavior in Disordered Nanoparticle Array

AbstractLarge, open‐gate transistors made from metal nanoparticle arrays offer possibilities to build new electronic devices, such as sensors. A nanoparticle necklace network (N3) of Au particles from 300 K to cryogenic temperatures exhibit a nonohmic I–Vd behavior, I ≈ (Vd–VT)ζ, where VT is a conduction gap and ζ is a constant critical exponent. The conduction gap in N3, made from disordered networks of 1D chains of 10 nm diameter Au particles exhibits room temperature (RT) gating. Although the I–Vd behavior at RT is identical to Coulomb blockade, the conduction is modulated by field‐assisted tunneling exhibiting classical critical behavior. In this study, based on three results, invariance of VT on gating, invariance of VT on temperature, and zero–bias conductance, a sharp transition temperature at ≈140 K is discovered where the conduction mechanism switches from Coulomb blockade to classical critical percolation behavior. The N3 architecture allows the reconciliation of the Coulomb blockade versus activation process as a sharp thermal transition to serve as a model system to study the exotic behavior in nanogranular‐metallic materials. The novel global critical behavior to local Coulomb blockade governed transition in these N3 architectures may potentially lead to novel sensors and biosensors.

On the classical critical behavior of the specific heat capacity of a model of structural phase transitions with a long-range interaction

The critical specific heat capacity c of a d-dimensional model describing structural phase transitions in an anharmonic crystal with a long-range interaction (decreasing at large distances r as r −d−σ , 0 < σ ≤ 2) is studied near the classical critical point Tc . At temperatures T > Tc and for dimensions σ < d < 2σ (σ and 2σ are the lower and the upper critical dimensions, respectively) the critical specific heat capacity is obtained in the form c ≈ 1 − Dεαs , where D > 0 and αs < 0 depend only on the ratio d/σ, and ε = T/Tc −1 is a measure of the deviation from the critical point. For three fixed values of the ratio d/σ the dependence c ≈ c(ε) is graphically presented. It is shown that at all temperatures T ≤ Tc the specific heat capacity retains its maximum value, c max = 1. The critical exponent αs , obtained here, coincides with that of the known mean spherical model, while c max is different for the two models.

Origin of mean-field behavior in an elastic Ising model

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical fluctuations of such a model. A mean field theory applied to the resulting effective Hamiltonian quantitatively accounts for both thermodynamics and kinetics observed in computer simulations, including a barrier to magnetization reversal that grows extensively with system size. For nanocrystals, which break translational symmetry, a straightforward extension of mean field theory yields similarly accurate results.

Criticalities in the itinerant ferromagnetUGe2

We provide a microscopic description of the magnetic properties of UGe$_2$ and in particular, of its both classical and quantum critical behavior. Namely, we account for all the critical points: the critical ending point (CEP) at the metamagnetic phase transition, the tricritical point, and the quantum critical end point at the ferromagnetic to paramagnetic phase transition. Their position agrees quantitatively with experiment. Additionally, we predict that the metamagnetic CEP can be traced down to zero temperature and becomes quantum critical point by a small decrease of both the total electron concentration and the external pressure. The system properties are then determined by the quantum critical fluctuations appearing near the instability point of the Fermi surface topology.

Minimal models for a superconductor-insulator conformal quantum phase transition

Conformal field theories do not only classify two dimensional (2D) classical critical behaviour, but they also govern a certain class of 2D quantum critical behaviour. In this latter case, it is the ground state wave functional of the quantum theory that is conformally invariant, rather than the classical action. We show that the superconducting-insulating (SI) quantum phase transition in 2D Josephson junction arrays (JJAs) is a (doubled) c = 1 Gaussian conformal quantum critical point. The quantum action describing this system is a doubled Maxwell–Chern–Simons model in the strong coupling limit. We also argue that the SI quantum transitions in frustrated JJAs realize the other possible universality classes of conformal quantum critical behaviour, corresponding to the unitary minimal models at central charge c = 1 − 6/m(m + 1) for m ⩾ 3.

Entanglement and quantum-classical crossover in the extended XX model with long-range interactions

In this work we considered the one-dimensional extended isotropic XY model (s=1/2) in a transverse field with uniform long-range interactions among the z components of the spins. We studied the classical critical behaviour of the model through the behaviour of the magnetization, isothermal susceptibility, internal energy and specific heat. We have obtained exact expressions for these functions and evaluated the critical exponents. The phase diagrams for the classical critical behaviour were built for three cases of the multiplicity p of the multiple spin interaction, namely p=2, p=3 and p→∞. We have also shown that the quantum phase transitions can also be characterized through two quantifiers of entanglement, namely, the concurrence and the von Neumann entropy. We have also verified through the von Neumann entropy how the central charge of the model is affected by the multiplicity p, the coupling exchange J2 and the uniform long-range interaction I.

Low-Dimensional Magnetic Systems

The interest in the nanoscale properties of low-dimensional magnetic systems has grown exponentially during the last decades and has attracted the attention of both experimentalists and theorists. The state of the art of these investigations has indeed allowed to give valuable insights into the underlying physics of complex magnetization dynamics driven by magnetic fields, electric currents and thermal effects. At the same time, such studies have found, in relatively short times, several applications at industrial level in the field of spintronics and magnonics as magnetic memories, microwave oscillators, modulators, sensors, logic gates, diodes and transistors. The goal of this special issue is to offer a variety of recent developments on this topic by gathering contributions arising from several specialists in the field of nanomagnetism. The strength of this issue lies indeed on its “variety”: the properties of these systems are, in fact, investigated from the viewpoint of physicists, engineers and mathematicians. Also, the issue encloses studies carried out at both mesoscopic and atomic scales, as well as results of both theoretical approaches (analytical, numerical and, in some cases, even “hybrid”) and experimental observations. The covered topics range from the micromagnetic modeling of domain wall motion, dynamics of vortex structures, phase-locking phenomena in spintronic oscillators, experimental techniques for realizing heterostructures based on magnon-induced spin transfer torque, band structure and exchange field in the Landau-Lifshitz equation for magnonic crystals, gap and gapless structures in fractional quantum Hall effect, semiclassical description of anisotropic magnets and classical critical behaviour of Heisenberg ferromagnets. More specifically, within the subject dealing with domain walls, for example, the structure of complex cross-tie/vortex wall structures in soft films has been studied in detail by using micromagnetic simulations whereas the influence of the Rashba spin-orbit coupling on the current-induced dynamics has been investigated analytically. Regarding the exchange interaction governing the dynamics in magnonic crystals, a full analytical calculation of the exchange field acting on spin-wave dynamics from themicroscopic Heisenbergmodel has been performed. Attention has been also devoted to the study of thermodynamics in the case of classical planar ferromagnets close to the zero-temperature critical point. Two reviews are also included in this special issue. The first one deals with two hybrid micromagnetic tools, based on Hamiltonian and Lagrangian approaches, to model the spin-dynamics in laterally confined magnetic systems. The second one is mostly devoted to the micromagnetic analysis of static and dynamic properties of magnetic domain walls in materials exhibiting perpendicular anisotropy.

Ultrasound velocity in dissolving alkali halide melts

Ultrasound velocities in the molten exsolving mixtures (LiF + CsCl, LiF + KBr, LiF + RbBr, LiF + CsBr, LiF + KI, LiF + RbBr, and LiF + CsBr) were obtained along the saturation line over a wide temperature range using the acoustic method. The temperature dependences of properties far away from the critical temperature are close to linear and the temperature and composition factors are highly correlated. The difference between the magnitudes of sound velocity for the coexisting phases increases with the radii of ions in the mixtures. The linearity of the temperature dependence of the velocity, which is typical for all systems at relatively low temperatures, is violated when approaching the critical point of mixing, mainly due to sharp changes of the light phase state. Our results suggested a classical (mean-field) critical behavior of ionic melts.

Quantum Griffiths Phase in the Weak Itinerant Ferromagnetic AlloyNi1−xVx

We present magnetization (M) data of the d-metal alloy Ni(1-x)V(x) at vanadium concentrations close to x(c) approximately = 11.4% where the onset of long-range ferromagnetic (FM) order is suppressed to zero temperature. Above x(c), the temperature (T) and magnetic field (H) dependencies of the magnetization are best described by simple nonuniversal power laws. The exponents of M/H approximately T(-gamma) and M approximately H(alpha) are related by 1-gamma = alpha for wide temperature (10 < T < or = 300 K) and field (H < or = 5 T) ranges. gamma is strongly x dependent, decreasing from 1 at x approximately = x(c) to gamma < 0.1 for x = 15%. This behavior is not compatible with either classical or quantum critical behavior in a clean 3D FM. Instead it closely follows the predictions for a quantum Griffiths phase associated with a quantum phase transition in a disordered metal. Deviations at the lowest temperatures hint at a freezing of large clusters and the onset of a cluster glass phase.

On the range of interaction from finite size scaling in magnetic Ni nanowires

A recent experiment reporting a thickness dependence of magnetic properties of Ni nanowires has been re-interpreted in terms of spin–spin interactions eventually ranging beyond nearest neighbors. An analysis following the Ginzburg argument indicated that the system is in the crossover regime from 3D Ising to classical critical behavior as a function of the normalized range of interactions R . The range of the interactions covering three to four coordination spheres of an Ni atom has been found by the fit to literature experimental data on Ni nanowires. Consistency with recent first-principles calculations are discussed.

Thermodynamics of volume-collapse transitions in cerium and related compounds

We present a non-linear elastic model of a coherent transition with discontinuous volume change in an isotropic solid. The model reproduces the anomalous thermodynamics typical of coherent equilibrium including intrinsic hysteresis (for a pressure driven experiment) and a negative bulk modulus. The novelty of the model is that the statistical mechanics solution can be easily worked out. We find that coherency leads to an infinite-range density–density interaction, which drives classical critical behavior. The pressure width of the hysteresis loop shrinks with increasing temperature, ending at a critical point at a temperature related to the shear modulus. The bulk modulus softens with a 1/2 exponent at the transition even far from the critical point. Many well known features of the phase diagram of Ce and related systems are explained by the model.

Observation of the crossover from quantum to classical critical behavior in ferromagnetic alloys of Pd 1− xNi x

The magnetization of Pd 1− x Ni x alloys was measured and the transition temperature T c was determined by Arrott plots. The critical concentration was found to be x c=0.022. For x⪢x c , T c indicates the Fermi liquid behavior, T c∼| x− x c| 1/2. Close to x c, on the other hand, T c follows a new power-law T c ∼|x−x c | zν (zν=1.6) , where ν is the static critical exponent and z the dynamic critical exponent. The quantum critical region for Pd 1− x Ni x is found to be ( x− x c)/ x c<0.1. These results suggest the evidence of the crossover from quantum to classical critical behavior in ferromagnetic alloys of Pd 1− x Ni x . We also derive the critical exponent β ∗ in ferro-to-paramagnet quantum-phase transition (FPQPT) from the concentration scaling for the magnetization M 0 (M 0∼|x−x c | β ∗ , β ∗=0.14) in the quantum critical region. We propose a new phase diagram for the itinerant electron ferromagnet Pd 1− x Ni x .

High-dimensional lattice gases

We investigate the critical behaviour of hard-core lattice gases in four, five and six dimensions by means of Monte Carlo simulations. In order to suppress critical slowing down, we use a geometrical cluster Monte Carlo algorithm. In particular, nearest-neighbour-exclusion lattice gases on simple hypercubic lattices are investigated. These models undergo Ising-like ordering transitions where the majority of the lattice-gas particles settle on one of two sublattices. A finite-size-scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour. The results agree with the renormalization predictions at and above the upper critical dimensionality. In particular, the predicted value of the Binder cumulant is confirmed.

Effects of instability of quantum critical behaviour in systems with quenched impurities

The one-loop renormalization group equations are derived and analysed for a wide class of quantum statistical models describing the critical behaviour of systems with short-range correlated random impurities. The classical and quantum critical properties are considered to first order in a double ε-expansion. It is proven that the quantum critical behaviour of disordered systems with short-range random correlation is equivalent to the classical critical behaviour of certain systems with extended random impurities. The reliability of the double ε-expansion method and the interpretation of the results are discussed.

Phase transitions in multicomponent liquid systems: The key role of electrolytes

Abstract

Mean-field critical behaviour of susceptibility near a curve of plait points in a ternary liquid mixture

We report on light scattering investigations in the vicinity of plait points in a ternary liquid mixture of ethanol + water + sodium carbonate. The plait points that were explored occur in the temperature range of 300 to 378 K. The coordinates of these points were extracted from the coexistence surface of the ternary liquid system. The approach to each of these plait points is quantified better by mean-field (or classical) critical behaviour (exponent γ = 1) than by 3-D Ising behaviour ( γ = 1.24). The role of electrolytes in modifying the anticipated 3-D Ising behaviour in this system is highlighted.

Crossover scaling in two dimensions

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the reduced temperature as well as in the finite-size crossover variable, it has up to now largely evaded a satisfactory numerical determination. Using a new Monte Carlo method, we could obtain accurate results for sufficiently large interactions ranges. Our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal. Also the so-called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region.

Classical critical behavior of spin models with long-range interactions

We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalization theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections at the upper critical dimension. We give both theoretical and numerical evidence that above the upper critical dimension the decay of the critical spin-spin correlation function in finite systems consists of two different regimes. For one-dimensional systems our estimates for the critical couplings are more than two orders of magnitude more accurate than existing estimates. In two and three dimensions we are unaware of any other results for the critical couplings.

Medium-range interactions and crossover to classical critical behavior.

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be observed.

Finite-size scaling and universality above the upper critical dimensionality.

According to renormalization theory, Ising systems above their upper critical dimensionality d_u = 4 have classical critical behavior and the ratio of magnetization moments Q = <m^2>^2 / <m^4> has the universal value 0.456947... However, Monte Carlo simulations of d = 5 Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorrect. We investigate this issue by simulation of a more general model in which d_u < 4, and a careful analysis of the corrections to scaling. Our results are in a perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.