Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

自旋交叉配合现象与分子电子器件

自旋交叉配合物在热、压力或光诱导自旋交叉现象的同时会伴随着其它一些协同效应，比如配合物颜色的改革、存在着大的热滞后效应等，这些协同效应是单个分子或分子集合体作为热开关、光开关和信息存储元件材料的基础。因此，自旋交叉配合物是开发新型的热开关、光开关和信息存储元件材料的理想分子体系。本文概述了自旋交叉现象的研究历史、现状和未来的发展趋势。讨论了影响配合物自旋交叉性质的各种内在的和外部的因素，总结了目前用于研究自旋交叉现象的各种现代测试技术。最后，展望了自旋交叉配合物在分子电子器件方面的应用前景。     

Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Forms of vibrations and structural changes in liquid state

Summary The forms of vibrations and displacements of particles in amorphous structures have been investigated. The particles, moving on highly non-linear amplitude, are responsible for the creation of disordered structures of amorphous bodies. The non-linear oscillators, even if 'few' in concentration, are characterized by unpredictable trajectories in phase space. The non-linear oscillators are fully developed in the liquid state above the crossover temperature T_cr and between T_cr and T_g their number decreases. Under T_g they completely disappear. The interconnection between the linear oscillators in blocks plays the most important role in the characteristic time spectra in liquid state. Using the additive properties of elements polarizibilities, the number of acoustical units in individual blocks at T_cr is estimated to be about 600 units. The diameter of blocks at T_cr was estimated to be about 1.8 nm. Even if the non-linear high amplitude motions disappear at solidification, the remnants of structural irregularity remain and the disordered structure of glass is formed.     

Spin crossover in polyaniline

Solutions of the basic form of polyaniline in m-cresol were studied by ESR and optical spectroscopy in the visible region. m-Cresol can slowly (during one month) protonate polyaniline. For the first time characteristic features of spin crossover were found: sharp changes in the magnetic susceptibility and the ESR line width of polyaniline at ∼200 and 250 K, a smooth decrease in the susceptibility and absorption with the temperature increase from 293 to 423 K, and the temperature hysteresis. The temperature-induced structural rearrangements of polyaniline are caused, most likely, by singlet-triplet transitions in relatively short sections of the polymer chain. The model of short sections permits to explain the origin of the temperature-independent part of susceptibility. Quantum-chemical calculations for the aniline dimers and tetramers describe correctly the singlet-triplet splitting value, thermochromism, and HFS constants in the spectrum of polyaniline. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1959–1966, October, 2007.     

The Role of Binary and Many-centre Molecular Interactions in Spin Crossover in the Solid State. Part I. Equation for Free Energy

Summary. A formalism has been developed that describes spin crossover equilibrium in the solid state by taking into account the effects of n nearest neighbours of a given molecule on its partition function. In this way binary and many-body interactions of the order n + 1 are included into the theoretical model and represented by non-ideality parameters connected with the splitting of free energy levels. Binary interactions are characterised by the main splittings whereas higher order interactions manifest themselves in asymmetries of splittings within multiplets. The contribution of molecular interactions can also be written in terms of formal excess free energies of the second, third, fourth and higher orders. Simple relationships between excess free energies and parameters of multiplets have been found for binary, ternary and quaternary interactions. This formalism is reduced to that of the model of binary interactions when effects of surroundings are additive leading to equidistant free energy multiplets. Higher order interactions may cause an abrupt spin crossover but in a limited range of compositions around the transition point. The regression of experimental transition curves of one-step spin crossover may yield estimates of excess energies up to the fifth order.     

Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.     

Multifunctionality in spin crossover materials

One of the most important trends in the spin crossover (SCO) field is focused on the synthesis of new molecule-based functional materials in which the SCO properties may be combined with other physical or chemical properties in a synergic fashion. The current stage of investigations regarding interplay and synergic effects between SCO, magnetic coupling, liquid crystalline properties, host-guest interactions, non-linear optical properties, electrical conductivity, and ligand isomerization is highlighted and discussed.     

Mixed-valence, mixed-spin-state, and heterometallic [2x2] grid-type arrays based on heteroditopic hydrazone ligands: synthesis and electrochemical features

An extended family of heterometallic [(M1)2(M2)2(L-)4](n+) [2x2] grid-type arrays 1-9 has been prepared. The three-tiered synthetic route encompasses regioselective, redox and enantioselective features and is based on the stepwise construction of heteroditopic hydrazone ligands A-C. These ligands contain ionisable NH and nonionisable NMe hydrazone units, which allows the metal redox properties to be controlled according to the charge on the ligand binding pocket. The 2-pyrimidine (R) and 6-pyridine (R') substituents have a significant effect on complex geometry and influence both the electrochemical and magnetic behaviour of the system. 1H NMR spectroscopic studies show that the Fe(II) ions in the grid can be low spin, high spin or spin crossover depending on the steric effect of substituents R and R'. This steric effect has been manipulated to construct an unusual array possessing two low-spin and two spin-crossover Fe(II) centres (grid 8). Electrochemical studies were performed for the grid-type arrays 1-9 and their respective mononuclear precursor complexes 10-13. The grids function as electron reservoirs and display up to eight monoelectronic, reversible reduction steps. These processes generally occur in pairs and are assigned to ligand-based reductions and to the Co(III)/Co(II) redox couple. Individual metal ions in the heterometallic grid motif can be selectively addressed electrochemically (e.g., either the Co(III) or Fe(II) ions can be targeted in grids 2 and 5). The Fe(II) oxidation potential is governed by the charge on the ligand binding unit, rather than the spin state, thus permitting facile electrochemical discrimination between the two types of Fe(II) centre in 7 or in 8. Such multistable heterometallic [2x2] gridlike arrays are of great interest for future supramolecular devices incorporating multilevel redox activity.