Premonitory effects near critical transition temperature in ordering systems – a Monte Carlo simulation

Premonitory effects manifest themselves in an ordering transition of the first kind (order) in the form of anomalously high short-range order (SRO) intensity at temperatures marginally above T _c, the critical transition temperature. This intensity located at the superlattice positions of the long-range ordered (LRO) phase is often attributed to the formation of ‘heterophase fluctuations’ resembling clusters of the LRO phase. Monte Carlo simulations in a hypothetical system showing FCC-to-L1₂ ordering transition have been carried out here to shed some light on this phenomenon and to look into the atomic configurations that make up these fluctuations.     

Linebroadening in DF-ODMR spectra of triplet excitons in the anthracene-1, 2, 4, 5-tetracyanobenzene single crystal near its structural phase transition

The temperature evolution of the DF-ODMR spectra of triplet excitons in the A-TCNB crystal has been studied in the vicinity of its order-disorder phase transition at T_c=204 K. Linewidth measurements were carried out for two selected orientations of the magnetic field in which the two crystal sites of the ordered phase appear as magnetically inequivalent and equivalent, respectively. In the former case the linebroadening observed near T_c was attributed to changes in the long-range order parameter and to the short-range clustering formation along the slacks. In the second case the sharp increase in the linewidth near T_c was interpreted and briefly discussed in terms of the critical slowing down of the fluctuations in the order parameter associated with the phase transition.     

Role of magnetism in the formation of a short-range order in iron-silicon alloys

The formation of a short-range order in soft magnetic Fe-Si alloys depending on the annealing temperature has been investigated theoretically and experimentally. The B2-type short-range order has been observed in samples quenched from temperatures T > T _C (where T _C is the Curie temperature) with the content c _Si close to the boundary of the two-phase region. Annealing at temperatures T < T _C for the content c _Si ≥ 0.08 leads to an increase in the fraction of regions with the D0₃-type short-range order. The mechanism of the formation of the short-range order in Fe-Si solid solutions has been analyzed by the Monte Carlo simulation with the ab initio calculated interatomic interaction parameters. It has been shown that the energy of the effective Si-Si interaction in bcc iron strongly depends on the magnetic state of the matrix. As a result, the B2-type short-range order is formed at T > T _C and is fixed at quenching, whereas the D0₃-type shortrange order is equilibrium in the ferromagnetic state. The results reveal the decisive role of magnetism in the formation of the short-range order in Fe-Si alloys and allow the explanation of the observed structural features of the alloys depending on the composition and temperature.     

Quasiequilibrium states of solid solutions

A phenomenological theory of quasiequilibrium states of solid solutions with at least three components is constructed under the assumption that the atomic mobilities of the components differ in order of magnitude. The short-range parts of the interatomic interactions are taken into account by introducing atomic self-volumes. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are derived neglecting the mobility of the least mobile component. It is shown that, for a nonuniform distribution of this component, the nonequilibrium critical temperature ceases being unique within the sample and acquires a local character. In consequence, opposing processes occur in the system in the temperature interval between T _c ^min and T _c ^max — homogenization in some sections and formation of interphase boundaries in others. Fiz. Tverd. Tela (St. Petersburg) 41, 60–63 (January 1999)     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT _s (>T _c), not at critical temperatureT _c. This occurs due to the anisotropy of such 2D systems.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T _c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T _c decay algebraically with critical exponent =1/4 and exponentially forT>T _c. If the critical temperature vanishes,T _c=0, we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln     

Mössbauer study of paramagnetic-like behavior below the Néel temperature in a random mixture Fe x Mn1−x TiO3 withx<0.3

As a part of studies of the microscopic behavior of spins in a mixed compound with competing exchange interactions Fe _x Mn_1–x TiO₃, the Mössbauer technique has been applied to the samples withx=0.05, 0.10 and 0.20 which establish the antiferromagnetic long-range order at the respectiveT _N's and do not show reentrant transitions at lower temperatures. We have found that in each of the three samples, the paramagnetic doublet superimposes on the magnetically split spectrum belowT _N. The peak intensity of the paramagnetic doublet decreases with decreasing temperature and the paramagnetic doublet becomes undetected as sharp peaks at a temperature aroundT _N/2. However, the spectra observed at temperatures lower thanT _N/2 suggest that the paramagnetic doublet still exists, though it is highly broadened. This is interpreted as that short-range clusters of spins fluctuating rather slowly with time coexist with the spins forming the antiferromagnetic long-range order. We consider that these short-range clusters are responsible for the existence of the paramagnetic component contributing to the magnetization versus temperature curve.     

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the (n) vector ϕ⁴ model, with long-range interaction decaying algebraically with the interparticle distance r like r ^{-d - σ}, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T _c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d _< = σ) and the upper ( d _> = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001     

Metal atom-induced diffuse scattering from short-range order among deuterium atoms in single crystal α-phase V2D

X-ray scattering has been studied above the critical ordering temperature, T_c (133°C), in b.c.c. α-phase V₂D. At 140 and 200°C quite weak diffuse intensity was observed centered on the reciprocal lattice points of the ordered superlattice. This intensity is due to short-range order among deuterium atoms which induces a local or short-range modulation of the parent vanadium lattice and suggests the possibility of local octahedral D—D fluctuations building up well above T_c.     

Role of magnetism in the formation of a short-range order in an Fe-Ga alloy

The formation of a short-range order in an Fe-Ga bcc alloy has been studied by Monte Carlo simulation with the use of effective interaction potentials calculated within the density functional theory for the ferromagnetic and paramagnetic states. It has been found that the pronounced short-range order of the D0₃ type is formed at Ga concentrations close to the boundary of the two-phase region at T < T _c, whereas no short-range order is observed at T < T _c. The results obtained are in agreement with the experimental X-ray diffraction analysis. The relation of the features of the short-range order in the Fe-Ga alloy to the magnetostriction value has been discussed.     

Electronic inhomogeneities,electron-lattice and pairing interactions in high-T c superconductors

The presence of electronic inhomogeneities strongly reduces the screening of the electron-ion interaction in high-temperature superconductors. This implies the existence of an non-totally screened long-range contribution to the electron-lattice coupling and opens an additional channel for the formation of copper pairs. We calculate the superconducting order parameter taking into account a) the longrange and the short-range parts of the electron-lattice interaction and b) the Coulomb repulsion between charge-carriers. We show that whereas the long-range electron-lattice coupling determines the anisotropy of the order parameter, the Coulomb repulsion and the short-range interactions determine its symmetry. Thus, different high-T _c superconductors may have s- or d-wave symmetry, depending on the relative strength of the interactions involved in the pairing.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Low energy electron diffraction beam profiles and phase transition at Si(111)-7 X 7 surface

Angular profiles of low energy electron diffraction (LEED) beams from Si(111)-7 × 7 are measured for various crystal temperatures T near the phase transition with apparent critical temperature T_c ≈ 1140 K. From analyses of the profiles it is concluded that (1) long range superstructure order persists for T up to at least 50 K above T_c and (2) with increasing T the correlation length characterizing the short-range order peaks for T ≈ T_c ? 100 K and decreases rapidly for T >T_c. Conclusion (1) is discussed with reference to a dislocation network model of Si(111)-7 × 7 reconstruction.     

面心立方格子上Ising自旋Ⅰ(1)的反铁磁性——配分函数的级数展开法

本文采用与文献[1]完全相类似的方法作出一般化Ising模型s=1在面心立方格子(fcc)上最近邻相互作用的反铁磁系统的统计理论,即用Pad近似式处理配分函数的高、低温幂级数有限项展开式,得出其反铁磁-顺磁转变为一阶相变。T_c=1.33J/k,小于(1/2)相应的相变点。文中算出了相关的热力学量如内能、潜热、熵、比热、长程和短程序参量,以及磁化率等。值得指出的是:(1)fcc上反铁磁-顺磁相变属于一阶,这是由格子密堆积的拓扑特征所决定,与s的大小无关;(2)T_c(s)随s的增加而缓慢地下降。 关键词：     

Modeling Order–Disorder Phase Transitions. Inclusion of the Range of Action of the Interatomic Interaction Potential

Results of a computer experiment simulating the atomic ordering process in a model alloy of stoichiometric composition AB and accounting for the range of action of the interatomic-interaction potential are analyzed. The effect of the range of action of the interaction potential (influence of the number of coordination spheres included in the interatomic interaction) on the disordering kinetics and on the order–disorder phase transition in the material at temperatures T _c between 0 and 1.1 (T _c is the temperature at which the atomic long-range order vanishes) is studied. The structure and energy features of atomic ordering are discussed. The objective necessity of accounting for long-range contributions in modeling order–disorder phase transitions and for the kinetics of temperature–induced ordering and disordering processes is examined.     

The vortex-like excitations detected by Nernst signals in high-Tc superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

Quantum bicriticality in Mn1 − x Fe x Si solid solutions: Exchange and percolation effects

The T-x magnetic phase diagram of Mn_{1 ? x} Fe _x Si solid solutions is probed by magnetic susceptibility, magnetization and resistivity measurements. The boundary limiting phase with short-range magnetic order (analogue of the chiral liquid) is defined experimentally and described analytically within simple model accounting both classical and quantum magnetic fluctuations together with effects of disorder. It is shown that Mn_{1 ? x} Fe _x Si system undergoes a sequence of two quantum phase transitions. The first “underlying” quantum critical (QC) point x* ～ 0.11 corresponds to disappearance of the long-range magnetic order. This quantum phase transition is masked by short-range order phase, however, it manifests itself at finite temperatures by crossover between classical and quantum fluctuations, which is predicted and observed in the paramagnetic phase. The second QC point x _c ～ 0.24 may have topological nature and corresponds to percolation threshold in the magnetic subsystem of Mn_{1 ? x} Fe _x Si. Above x _c the short-range ordered phase is suppressed and magnetic subsystem becomes separated into spin clusters resulting in observation of the disorder-driven QC Griffiths-type phase characterized by an anomalously divergent magnetic susceptibility χ ～ 1/T ^ξ with the exponents ξ ～ 0.5–0.6.