The zero-distribution of the great partition function in the complex fugacity plane of gases of point particles with logarithmic interaction

The equation of state for gases of point particles with logarithmic interaction is derived. The system exhibits a phase transition at a critical temperature T_c. The critical temperature is a function of the dimension of the system. A hard core must be added below T_c to prevent the system from collapsing. The specific heat diverges on both sides as |T_c - T|^-2 in any dimension.For T≤T_c there are no zeros of the grand partition function in the complex fugacity plane, for T >T_c all zeros occupy the whole negative real axis. The density of zeros will be calculated.     

One-dimensional spin glass with oscillating long-range interaction

In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κV _O cosQ x exp (?κ|x|), where κ?c?Q (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT _c =cV ₀, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofT _c (|τ?(κ/c)^2/3) and at very low temperaturesT?κV ₀ when a gap appears in the distribution of the molecular fielsh ath≈0.     

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.     

AC susceptibility and temperature modulation studies of gadolinium near the Curie point

Measurements of the ac susceptibility and temperature modulation studies of the ac and dc magnetic properties of polycrystalline gadolinium in the vicinity of the Curie point T_c are reported. Field-independent exchange-enhanced paramagnetism was observed above T_c. Below T_c the initial field-independent susceptibility was observed for applied fields < 8 A/m rms and exhibited a frequency dependence characteristic of a magnetic after-effect. Within about 3 K of T_c this susceptibility is strongly influenced by domain nucleation and a temperature dependent magnetic relaxation time was observed.     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

Spontaneous symmetry breaking in massless field theories,finite temperature and criticality

We study the behaviour at finite temperature of massless field theories exhibiting spontaneously broken solutions. We establish the occurence of a phase transition of the first kind at some critical point T_c which can be calculated to any finite order in perturbation theory. Similarly, perturbative methods can be used for thermodynamic functions in all regions, including the critical region. For the case of a gauge theory, we demonstrate the gauge independence of the critical point, the thermodynamic potentials and the order parameter to all orders of perturbation theory.     

Critical hyper-Raman scattering in ferroelectrics

It is shown, that the critical hyper Raman scattering (CHRS) due to the polarization fluctuations in ferroelectrics must increase sharply in the vicinity of the phase transition point T_c. The spectral intensity of the CHRS is expressed explicitely in terms of the imaginary part of low-frequency dielectric permeability ε(ω, T) which permits to use the CHRS for investigations of the critical dynamics near T_c, in particular, in centrosymmetric phase, where the ordinary Raman scattering (of the first order) is forbidden. The calculated CHRS intensity in the BaTiO₃ type crystals is found to be larger by 4–5 orders of magnitude than that in the media investigated earlier.     

Effect of irradiation at low doses and incubation of voids within the rate theory approach

The evolution of defects in a material under irradiation is studied at low doses (∼5 dpa or less) using rate equations. It is shown that as a function of temperature at a critical valueT _c a transition occurs in the behaviour of the solutions of the rate equations. BelowT _c the voids show incubation effects. An expression is derived for the critical dislocation density at which the void growth starts. This is related to the trapped vacancy fraction ε in vacancy dislocation loops. AboveT _c the incubation effects are shown to be related to the gas production rate which becomes the rate controlling parameter in determining the evolution of the defects. A gas-bubble to void transition occurs at a critical void radius and expressions are derived for the critical void size and dose at which the transition appears. It is shown that closely related to this is the incubation dose for interstitial loops. Finally, these features are corroborated by actual numerical integration of the rate equations.     

Width of the zero-field superconducting resistive transition in the vicinity of the localization threshold

Resistive superconducting zero-field transition in amorphous In-O films in the states in the vicinity of the insulator-superconductor transition is analyzed in terms of two characteristic temperatures: the upper T _c0 , where the finite amplitude of the order parameter is established, and the lower T _c , where the phase ordering takes place. It follows from the magnetoresistance measurements that the resistance in between, T _c <T< T _c0 , cannot be ascribed to the dissipation by thermally dissociated vortex pairs. So, it is not a Kosterlitz-Thouless-Berezinskii transition that occurs at T _c .     

Universality of the ratio of the critical amplitudes of the magnetic susceptibility in a two-dimensional ising model with nonmagnetic impurities

The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q _c = 0.407254). The behavior of the effective critical exponent γ(q) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.     

Central peak for a scalar ϕ 4-model: mode coupling approach revisited

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T _c. For a scalar ? ⁴-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T _c'(≥ T _c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ? ⁴- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T ₀'obtained from the Ginzburg criterion sets an upper bound for T _c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.     

Spin crossovers in Mott–Hubbard insulators at high pressures

The high-pressure induced phase transitions initiated by electronic transition in 3d ions from the high-spin (HS) to the low-spin (LS) state (HS-LS spin-crossover) are considered. Behavior of the system with d⁶ electronic configuration is investigated in the ground state of zero temperature and critical pressure P_c. Magnetic properties of the Mott–Hubbard insulator (Mg_1−xFe_x)O are studied in the vicinity of the quantum critical point (T=0, P_c). At the critical pressure of spin crossover P_c, the spin gap energy ε_S between HS and LS states is zero. The quantum spins fluctuations HS⇔LS do not require any energy, and the antiferromagnetism is destroyed in the quantum critical point by the first order transition.     

Preparation and magnetic properties of LaMnO3 + δ (0 ≤ δ ≤ 0.154)

The structural, electrical, and magnetic properties of ceramic perovskite manganites LaMnO_{3 + δ} (δ = 0–0.154) are investigated. It is found that, in a weak magnetic field (B = 2 G), the LaMnO_{3 + δ} manganite with δ = 0.065 at temperatures below the Curie temperature T _C of the paramagnet-ferromagnet phase transition has a mixed (spin glass + ferromagnet) phase. In LaMnO_{3 + δ} manganites with the parameter δ = 0.100–0.154, this phase transforms into a frustrated ferromagnetic phase. A similar transformation was observed previously in La_1?x Ca_xMnO₃ compounds at calcium contents in the range 0 ≤ x ≤ 0.3. This similarity is explained by the fact that, in both materials, the Mn⁴⁺ concentration and, accordingly, the hole concentration c change equally in the concentration range from ～0.13 to 0.34 with an increase in x or δ. However, the magnetic irreversibility, the concentration dependences of the Curie temperature T _C(c) and the magnetic susceptibility X(c), and the critical behavior of the temperature dependence of the susceptibility X(T) in the vicinity of the Curie temperature T _C differ substantially for these two materials. The observed differences are associated with the distortion of the cubic perovskite structure, the decrease in the degree of lattice disorder, and a more uniform distribution of holes in the LaMnO_{3 + δ} manganites as compared to the La_{1 ? x} Ca_xMnO₃ compounds.     

Critical point wetting: The effect of hydrodynamical and steric interfacial interactions

It is shown for the first time that the capillary waves and hydrodynamic correlations in an adsorbed film of a simple fluid provide incomplete wetting in some vicinity of the critical point T_c. On approaching T_c the film thickness grows infinitely and the wetting angle tends to zero due to the steric repulsion between the film-bulk fluid interface and the substrate.     

Anomalous states of the crystal structure of (Rb0.1(NH4)0.9)2SO4 solid solutions in the temperature range 4.2–300 K

Crystals of (Rb_0.1(NH₄)_0.9)₂SO₄ solid solutions are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameter a exhibits an anomalous behavior, namely, the “invar effect” at temperatures above the ferroelectric phase transition point T _c and an anomalous increase in the temperature range from T _c to the liquid-helium temperature. An anomalous increase in the lattice parameter a and an increase in the intensity of Bragg reflections with a decrease in the temperature are interpreted within the model of the coexistence of two sublattices hypothetically responsible for the ferroelectric phase transition. A series of superstructure reflections observed along the basis axes corresponds to a sublattice formed in the matrix of the host structure. Analysis of the ratio between the lattice parameters of these structures allows the inference that, in the temperature range 4.2–300 K, the structure of the crystal under investigation can be considered an incommensurate single-crystal composite.     

Critical properties of the paramagnetic-to-ferromagnetic transition in nanocrystalline Gd diluted with Fe

Nanocrystalline Gd_0.946Fe_0.054 of average grain size 68 nm was prepared by melt-spinning. The magnetic behavior in the vicinity of the paramagnetic to ferromagnetic transition was investigated via dc magnetization and ac susceptibility measurements. The transition temperature and effective critical exponents for the order parameter and zero-field susceptibility were determined using Arrott-Noakes and Kouvel-Fisher analyses. The values obtained were T_C=291.71±0.07 K, β_eff=0.385±0.009, and γ_eff=1.24±0.03, respectively. Correction to scaling analysis indicated that the asymptotic exponents were both smaller than the effective ones within the reduced-temperature range investigated, contrary to the behavior seen in monocrystalline Gd. This behavior can be explained in terms of a crossover from 3D short-range Heisenberg universality class to the 3D Ising universality class due to increased anisotropy induced by the high magnetic fields used in the measurements and also possibly due to strain.     

Heat capacity anomaly in the vicinity of the tricritical and upper critical points

The anomalous behavior of the isochoric heat capacity of a mixture of methane, pentane and heptane is studied experimentally in the vicinity of the liquid-vapor critical point in the cases when (a) the critical temperature T _c approaches the tricritical point T _TCP and (b) the critical temperature approaches the upper critical end point T _U . It is shown that in all cases, the singular part of the heat capacity of the mixture has the form C_sing=A¦τ¦^?α, where τ=(T ? T _c )/T _c and α≈0.11. When T _c →T _U , amplitude A of the heat capacity anomaly is found to be approximately constant. At the same time, the amplitude of the anomaly tends to zero in the vicinity of the tricritical point: A∝¦τ_c¦^ε, where τ_c=(T _c ? T _TCP )/T _TCP and ε=1.6?1.7. The inevitable vanishing of this mode of the heat capacity anomaly leads to a negative value of the critical index \(\tilde \alpha\) characterizing the heat capacity anomaly at the tricritical point, while the tricritical point theory and the isomorphism hypothesis predict \(\tilde \alpha = 0.5\).     

Specific heat behaviour of the ferroelectric PbHPO4

Specific heat measurements of PbHPO₄ confirm the second order character for the Ferro-paraelectric phase transition at T_c = 307.75 ± 0.09 K. A comparison between the experimental results and phenomenological and statistical theories is carried out. The classical critical behaviour for both α₊ and α_- are shown to be valid up to |T ? T_c| < 0.1K.     

Diamagnetic susceptibility near the surface or twinning plane at the transition to the superconducting state

Besides the well-known bulk fluctuation contribution to the diamagnetic susceptibility there is an additional surface contribution with the singularity at T_SH exceeding the superconducting bulk transition temperature T_c(H). The results obtained allow to explain the anomalous behavior of the diamagnetic susceptibility found by Khaikin and Khlyustikov.