Critical behavior of dilute electrolyte solutions

A theory of the critical behavior of a dilute ionic solution is constructed. An expression for the susceptibility in a wide temperature range is obtained. It is shown that ionic solutions belong to the universality class of the Ising model. The Ginzburg parameter of the ionic solutions decreases with the increase of the solvent concentration. In the general case, the critical exponent of susceptibility nonmonotonically depends on the temperature in the crossover region from the Ising-like to the mean-field behavior. In the vicinity of the transition point, the Debye-Hückel screening radius is proportional to the correlation length. As T→T _c, the screening radius tends to infinity and the screening disappears. The voltage between the two phases of the ionic solution is proportional to the order parameter and changes as |T/T _c?1|^β in the vicinity of the phase transition point.     

Influence of structural relaxation of scaling law analysis at the ferromagnetic transition of amorphous alloys

In this paper we report the influence of structural relaxation upon the ferromagnetic transition, T_c, and the possible attendant consequences on the scaling law analyses for amorphous (Fe_xNi_1?x)₇₅P₁₆B₆A1₃ alloys. Despite changes in T_c with thermal annealing, consistent values for the critical exponents (β ? 0.4, δ ? 5.1, γ ? 1.6) are observed.     

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

We study the statistical properties of the sum S _t = dt'σ _t', that is the difference of time spent positive or negative by the spin σ _t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of S_t and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( T > T _c), criticality ( T = T _c), and low temperature ( T < T _c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S _t/t was always larger than the equilibrium magnetization is found to decay as t ^{- - ?}. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model. Received 4 December 2000     

Crossover scaling,correlation function and connectivity in dilute low temperature ferromagnets

For quenched dilute ferromagnets with a fractionp of spins (nearest neighbor exchange energyJ) and a fraction 1 —p of randomly distributed nonmagnetic atoms, a crossover assumption similar to tricritical scaling theory relates the critical exponents of zero temperature percolation theory to the low temperature critical amplitudes and exponents near the critical lineT _c (p)>0. For example, the specific heat amplitude nearT _c (p) is found to vanish, the susceptibility amplitude is found to diverge forT _c (p →p _c ) → 0. (Typically,p _c =20%.) AtT=0 the spin-spin correlation function is argued from a droplet picture to obey scaling homogeneity but (at fixed distance) not to vary like the energy; instead it varies as const + (p _c —p)^2β +? for fixed small distances. A generalization of the correlation function to finite temperatures nearT _c (p) allows to estimate the number of effective percolation channels connecting two sites in the infinite (percolating) network forp>p _c ; this in turn gives, via a dynamical scaling argument, a good approximation for theT=0 percolation exponent 1.6 in the conductivity of random three-dimensional resistor networks. This channel approximation also givesΦ=2 for the crossover exponent; i.e. exp(?2J/kT _c (p)) is an analytic function ofp nearp=p _c . An appendix shows that cluster-cluster correlations atT=0 (excluded volume effects) are responsible for the difference between percolation exponents and the (pure) Ising exponents atT _c (p=1).     

Test of scaling theories for metal-insulator transition in amorphous,superconducting BixKr1−x mixtures

Measurements of the d.c. electrical conductivity σ and the superconducting transition temperature T_c in amorphous Bi_xKr_1?x mixtures as a function of the Bi concentration x give clear evidence for the occurence of an Anderson or Anderson-Mott type metal-insulator transition at x_c = 0.55 ± 0.02. From our σ and T_c data we estimate two characteristic exponents which we compare with those derived from existing scaling theories for the metal-insulator transition in disordered systems.     

A nonconventional approach to describe classical-quantum crossover phenomena near criticality

A nonconventional renormalization group procedure, which involves fixed points and eigenvectors depending on temperature T, is proposed to describe classical-quantum crossover phenomena for quantum systems near criticality. In this new picture, T-dependent critical exponents occur, where T assumes the role of a natural crossover parameter.     

The concentration dependence of the ferroelectric transition temperature of the solid solution of TSCC and TSCB

The concentration dependence of the ferroelectric transition temperature T_c of single crystals of the solid solution tris-sarcosine calcium chloride_1?x bromide_x is studied experimentally by measurement of the static dielectric constant ?_b and described by the empirical relation $\text{T}{}_{\mathrm{c}}\text{(X) = T}{}_{\mathrm{c}}\text{(0) [1?(X/X}{}_{\mathrm{c}}\text{)]}\text{1}\text{2}$. The Ising model with transverse field and the model of coupled anharmonic oscillators are used to explain the concentration dependence of the transition temperature T_c.     

Possible relationship between Cu-NQR frequencies and Cu valence states in CuO2-planes for high-T c superconductors

We report on⁶³Cu-NQR frequency ν_NQR measurements on various high-T _c superconductors. An empirical relationship betweenT _c and ν_NQR is presented. We attribute this finding to variations in the valence state of the in-plane Cu ions which, due to the unusual electric polarizability of the O^2? ions, depends sensitively on the Cu?O distance.     

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.     

The effect of quenched bond disorder on first-order phase transitions

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin–Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to 128×128$128\times 128$ spins, each of which is represented by three colors taking values ±1$\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, ν$\nu$, and the magnetization critical exponent, β$\beta$, from finite size scaling analysis. We find that the critical exponents, ν$\nu$ and β$\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.     

Gaussian free field in the background of correlated random clusters,formed by metallic nanoparticles

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T ? T _c . The fractal dimension of iso-potential lines (D _f ), the exponent of the distribution function of the gyration radius (τ _r ), and the loop lengths (τ _l ), and also the exponent of the loop Green function x _l change in terms of T ? T _c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D _f (T) ? D _f (T _c ) ~ 1/√ξ(T), in which ξ(T) is the spin correlation length in the Ising model.     

Finite size scaling of spin-spin correlations on the Ising square lattice

Using Monte Carlo data for the Ising square lattice, we show that the row spin-spin correlation functions scale as a function of both lattice size and ? = ∣1 ? T/T_c∣ forT >T_c.     

On the maximum of the k-dependent susceptibility for fixed k and T > Tc

We study the maximum occuring in ${}_{\mathrm{x}}\text{(}\text{k}\text{, T)}$ for fixed k at a temperature T_max > T_c. We examine the predictions of both Ornstein-Zernike and ?-expansions for the position of this maximum. These are compared with the exact results fot the two-dimensional Ising model.     

Polarization properties of Li2−x Na x Ge4O9 (0.2 ≤ x ≤ 0.3) crystals

The polarization switching in sinusoidal fields and the pyroelectric properties of Li_2?x Na _x Ge₄O₉ (0.2 ≤ x ≤ 0.3) crystals are measured in the temperature range T _c ?T ≤ 40 K. The behavior of the P?E hysteresis loops with variations in temperature is investigated for crystals with phase transition temperatures T _c < 300 K and T _c > 300 K. It is shown that, for crystals with phase transition temperatures T _c < 300 K, the temperature dependence of the hysteresis loop exhibits a behavior typical of crystals with second-order phase transitions. The crystals with phase transition temperatures T _c > 300 K are characterized by double hysteresis loops in the temperature range T _c ?T ₁ ≈ 30 K. The correlation between the polarization properties and possible structural transformations of the Li_2?x Na _x Ge₄O₉ crystals due to the change in the concentration ratio of Na and Li ions is discussed.     

Superconducting and normal state properties of Ag1−xSn1 + xSe2−y

The occurrence of superconductivity in a new ternary non-transition element compound with the cubic NaCl structure is reported. The composition of this compound is Ag_1?xSn_{1 + x}Se_2?y, with a maximum homogeneity range given by ?0.02 ?x?0.24 and 0 ? y ?0.1. The superconducting transition temperature (T_c) ranges from a minimum of 4.5 K for x = ?0.02, y = 0 to a maximum of 6.9 K for x = 0.24,y = 0. These T_c's are higher than previously observed in nontransition element NaCl structure compounds. Electrical resistivity data show a positive temperature coefficient, and room temperature magnetic susceptibility measurements reveal a rapidly increasing density of states at the Fermi level with increasing x. Two ionic models for calculating the carrier concentration of Ag_1?xSn_{1 + x}Se_2?y are discussed, and a third model based on the band picture is proposed. The composition dependence of the magnetic susceptibility was used to test the validity of each of the models.     

Superconducting transition temperatures of the system V1−xTixHy

T_c measurements for V_1?xTi_xH_y show that a decrease in T_c always occurs upon hydrogenation, but with slopes ($\text{?T}{}_{\mathrm{c}}\text{?y}\text{)}{}_{\mathrm{x}}$ that change with x. A phenomenological model is suggested, associating the T_c decrease in most of the range of x to changes in nominal number of conducting electrons and in the volume induced by the hydrogenation. The model roughly accounts for the variations in T_c in the V-rich alloys. It fails to explain the T_c variation at the Ti end.     

Thermodynamic properties of the φ4 lattice field theory near the Ising limit

For a d-dimensional φ⁴ lattice field theory consisting of N spins with nearest-neighbor interactions, the partition function is transformed for large bare coupling constant λ into an Ising-like system with additional neighbor interactions. For d = 2 a mean field approximation is then used to estimate the difference in critical temperature between the lattice φ⁴ field theory and its Ising limit (λ = ∞). Expansions are obtained for the susceptibility and specific heat. The critical exponents are shown to be identical to the Ising exponents.     

Electrical resistivity and the phase transition temperatures of Ti1−xHfxSe2 mixed crystals

The onset temperature of the superlattice T_c developed in the mixed system Ti_1-xHf_xSe₂ is determined from measurements of the electrical resistivity. As x is increased, the onset temperature T_c reaches the maximum around x?0.07 before the superlattice formation is completely suppressed around x?0.35. The functional dependence of T_c(x) can be interpreted by considering TiSe₂ as an excitonic insulator.     

Observation of a transition from BCS to HTSC-like superconductivity in Ba1 − x KxBiO3 single crystals

The temperature dependences of the upper critical field B _c2(T) and surface impedance Z(T) = R(T) + iX(T) have been measured in Ba_{1 ? x} K_xBiO₃ single crystals with transition temperatures 6 ≤ T _c ≤ 32 K (0.6 > x > 0.4). A transition from the BCS to an unusual type of superconductivity has been revealed: B _c2(T) curves of the crystals with T _c > 20 K have positive curvature (as in some HTSCs), and those of the crystals with T _c < 15 K described by the usual Werthamer-Helfand-Hohenberg (WHH) formula. The R(T) and X(T) dependences of the crystals with T _c ≈ 32 K and T _c ≈ 11 K in the temperature range T ? T _c are linear (as in HTSCs) and exponential (BCS), respectively. The experimental results are discussed using the extended saddle point model by Abrikosov.