Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

The Curie temperature of dilute ferromagnetic alloys near the percolation threshold

Upper limit for the Curie temperature T_c(x) of the dilute Heisenberg ferromagnet near percolation threshold is derived. Qualitative arguments are put forward that this limit gives a correct dependence of T_c on the concentration of magnetic atoms x.     

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N_τ = 4, 6 and 8 and spatial extent N_σ = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T_c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N_τ = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32⁴ lattices to fix the temperature scale. An extrapolation to the continuum limit yields T_c/√σ = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at T ≅ 5T_c. For the spatial string tension we find √σ_s/T=0.566(13)g²2(T) with g² (5T_c) ≅ 1.5.     

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n _h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n _h (A, t) = 2c _h /(A + λ _h t)², demonstrating the validity of dynamical scaling in this system. Here $ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-0em} 8}\pi \sqrt 3 $ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ _h is a material parameter. The distribution of domain areas, n _d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ _h t. Identical forms are obtained for coarsening from a critical initial state, but with c _h replaced by c _h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c _h . By applying a ‘mean-field’ type of approximation we obtain the form n _d (A, t) ? 2c _d [λ _d (t+t ₀)] ^τ?2/[A+λ _d (t+t ₀)] ^τ , where t ₀ is a microscopic timescale and τ = 187/91 ? 2.055, for a disordered initial state, and a similar result for a critical initial state but with c _d → c _d /2 and τ → τ _c = 379/187 ? 2.027. We also find that c _d = c _h + O(c _h ² ) and λ _d = λ _h (1 + O(c _h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.     

Phase boundary of dilute lattice spin glasses

Based on a recently developed algorithm for the exploration of ground states in bond-diluted lattice spin glasses, we determine the scaling of defect energies with system size for Ising spin glasses at the bond percolation threshold p_c. The results can be related by well-known scaling relations to the shape of the transition temperature T_g∼(p-p_c)^φ between the paramagnetic and glassy regime for p→p_c. The numerical results in three dimensions are consistent with rather old experimental data for (Fe_xNi_1-x)₇₅P₁₆B₆A₃, suggesting that new experimental work may be able to put those numerical predictions to the test.     

On the characterization of periodic signals using third-order statistical functions

In this paper the theoretical errors involved in the determination of a parameter by measuring g(³)(T,τ,τ') and n⁽³⁾(T) are pointed out. The values of this errors are calculated and compared with those obtained by measuring g(²)(T,τ) for a particular case.     

Fluctuation pressure of membrane between walls

We prove that a tensionless membrane, fluctuating harmonically with free ends between two parallel plates of spacing 2d. generates a pressure of the functional form p = (T/Ad)τa(τ), where τ is the dimensionless variable τ ≠ (T/κ)A/d², κ is th curvature elastic constant, and A the area of the plates. For large A, a(τ) becomes a constant which we determine by Monte Carlo simulation to be a_∞ = 0.060±0.003.     

Non-equilibrium structure factor for the disordering of adsorbed monolayers

We consider the non-equilibrium, time-dependent elastic-scattering structure factor S(q,t), for the disordering of an ordered overlayer, initially in equilibrium at temperature T_I and characterized by the structure factor S(q,0)=x(q,T_I, upon a sudden increase in temperature T_I→T_F at constant coverage, such that the adsorbates equilibrate at T_F in a disordered phase. The initial decay of a peak in x(q,T_I) proceeds exponentially in time, $\text{exp}\text{(−}\text{t}\text{τ}{}_{\mathrm{q}}\text{)}$, where τ_q is a wavevector-dependent lifetime, before it crosses over to a power-law, t⁻¹ decay. When x(q,T_I) is peaked at the boundaries of the Brillouin zone (BZ), the peak approximately maintains its shape in q-space as it decays exponentially. Except near the center of the BZ, after the peak has decayed sufficiently, the dependence of S(q,t) on q is as though the spins quasi-equilibrate to the equilibrium structure factor associated with T_F, x(q,T_F), in that the ratio $\text{S(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ is independent of q, is dependent on time, approaching unity as t⁻¹ for large t. For systems exhibiting an initial peak for q ≈ 0, the peak decays exponentially but does not preserve its shape, since τ_q strongly depends on q, diverging as q⁻² for q→0. For these systems too, away from the center of the BZ, $\text{S}\text{(q,t)}\text{x(q,T}{}_{\mathrm{<mtext>F</mtext>}}\text{)}$ rapidly evolves to a slowly decaying function of $\text{t}\text{t}{}_{\mathrm{w}}$, independent of q. In this case, however, the characteristic time scale, t_w, is anomalously long, proportional to ξ², where ξ is the correlation length associated with the initial state. This behavior of t_w can be related to the random walk of domain boundaries.     

Exciton-magnon interactions in NicMg1−c O single crystals

The effect of chemical composition and temperature on exciton-magnon interactions in Ni_cMg_1?c O single crystals was studied using optical absorption spectra in the region of the magnetic-dipole ³ A _2g (G)→³ T _2g (F) and electric-dipole ³ A _2g (F)→¹ E _g (D) transitions. The two zero-phonon lines at ～7800 and ～7840 cm^?1 on the low-energy side of the magnetic-dipole transition band were assigned to a pure exciton transition and an exciton-one-magnon transition at the center of the Brillouin zone. The intensity of the exciton-one-magnon peak decreases rapidly with increasing magnesium ion concentration and/or temperature, to vanish altogether at T=6 K for c<0.95 and at T=130 K for c≥0.99. Thus, the contribution of long-wavelength magnons in optical absorption spectra of Ni_cMg_1?c O becomes negligible at temperatures substantially lower than the Néel point T _N (the antiferromagnetic ordering temperature). This observation can be explained as being due to a substantial decrease in the characteristic spin-spin interaction length with increasing concentration of the diamagnetic magnesium impurity ions (static disorder) and/or with increasing amplitude of thermal atomic vibrations (dynamic disorder). At the same time, the peak at ～14500 cm^?1, which lies in the electric-dipole transition region and corresponds to excitation of an exciton and two magnons at the Brillouin zone edge, remains visible up to the Néel temperature. This is accounted for by the short-wavelength magnons being sensitive to short-range magnetic order, which persists up to T _N .     

Mixed alkali effect in borate glasses—EPR and optical absorption studies in xNa2O–(30−x)K2O–70B2O3 glasses doped with Mn2+

The mixed alkali borate xNa₂O–(30−x)K₂O–70B₂O₃ (5≤x≤25) glasses doped with 1 mol% of manganese ions were investigated using EPR and optical absorption techniques as a function of alkali content to look for ‘mixed alkali effect’ (MAE) on the spectral properties of the glasses. The EPR spectra of all the investigated samples exhibit resonance signals which are characteristic of the Mn²⁺ ions. The resonance signal at g≅2.02 exhibits a six line hyperfine structure. In addition to this, a prominent peak with g≅4.64, with a shoulder around g≅4.05 and 2.98, was also observed. From the observed EPR spectrum, the spin-Hamiltonian parameters g and A have been evaluated. It is interesting to note that some of the EPR parameters do show MAE. It is found that the ionic character increases with x and reaches a maximum around x=20 and thereafter it decreases showing the MAE. The number of spins participating in resonance (N) at g≅2.02 decreases with x and reaches a minimum around x=20 and thereafter it increases showing the MAE. It is also observed that the zero-field splitting parameter (D) increases with x, reaches a maximum around x=15 and thereafter decreases showing the MAE. The optical absorption spectrum exhibits a broad band around ∼20,000 cm⁻¹ which has been assigned to the transition ⁶A_1g(S)→⁴T_1g(G). From ultraviolet absorption edges, the optical bandgap energies and Urbach energies were evaluated. It is interesting to note that the Urbach energies for these glasses decrease with x and reach a minimum around x=15. The optical band gaps obtained in the present work lie in the range 3.28–3.40 eV for both the direct and indirect transitions. The physical parameters of all the glasses were also evaluated with respect to the composition.     

Dynamic and spatial behavior of a corrugated interface in the driven lattice gas model

The spatiotemporal behavior of an initially corrugated interface in the two-dimensional driven lattice gas (DLG) model with attractive nearest-neighbors interactions is investigated via Monte Carlo simulations. By setting the system in the ordered phase, with periodic boundary conditions along the external field axis. i.e. horizontal, and open along the vertical directions respectively, an initial interface was imposed, that consists in a series of sinusoidal profiles with amplitude A₀ and wavelength λ set parallel to the applied driving field axis. We studied the dynamic behavior of its statistical width or roughness W(t), defined as the root mean square of the interface position. We found that W(t) decays exponentially for all λ and lattice longitudinal sizes L_x, i.e., the lattice side that runs along the axis of the external field. We determined its relaxation time τ, and found that depends on λ as a power law τ∝λ^p, where p depends on the temperature and L_x. At low T’s (T?T_c(E)) and large L_x, p approaches to p=3/2. At intermediate T’s (T<T_c(E)), p decreases up to p≈1, and is free of finite effects. This indicates that the interface stabilizes faster than in the equilibrium model, i. e. the Ising lattice gas (E=0) where p=3. At higher T’s p increases for T?T_c(E), and the finite size dependence is recovered. Also, if T is fixed, p increases with L_x until it saturates at large values of it, while this regime is vanishing at T?T_c(E). In this way, the dynamic relaxation process of a sinusoidal interface is improved by the external driving field with respect to its equilibrium counterpart, if the system is set in an intermediate temperature stage far from T_c(E) and in a lattice with a sufficiently large longitudinal side. The behavior of τ was also investigated as a function of E and in the intermediate stage T<T_c(E). It was found that τ decreases exponentially with E in the interval 0<E?1, while for higher fields it remains constant. The exponential decay depends on the wavelength of the initial profile.In order to study the spatial evolution of the profiles, we evaluated the structure factor of the interface, and the Fourier coefficients corresponding to the same wave vector of the initial profile. The obtained results allowed us to conclude that the spatial evolution of the profile maintains its initial wavelength, does not travel along the external field axis, and its shape is preserved over all the relaxation process.     

Lifetimes of Rydberg states in ions of the group II elements

Total probabilities A _nl of spontaneous radiative transitions, which determine lifetimes τ _nl = 1/A _nl of nS-, nP-, nD- and nF-states in singly charged ions of the group IIa (Be⁺, Mg⁺, Ca⁺, Sr⁺, Ba⁺) and IIb (Zn⁺, Cd⁺, Hg⁺) elements, were calculated in the single-electron Fues’ model potential (FMP) method. An asymptotic dependence is determined for highly excited states with small angular momentums and presented in the form τ _nl = τ _l ⁽⁰⁾ n ³ Q _l (1/n) and numerical values of the factors τ _l ⁽⁰⁾ and coefficients of the cubic polynomial Q _l (x) are calculated, which approximate results of numerical computations with relative error below 2% in the range of states with principal quantum numbers from n = 7 to n ≈ 2000. The comparison of the numerical results with data in literature is presented, and applicability and reliability of single-electron model calculations are discussed in detail for positive singly charged ions of the group II elements.     

Anionic conductivity and thermal stability of single crystals of solid solutions based on calcium fluoride

The temperature and composition dependencies of the anionic conductivity in the temperature range from ambient to 1073 K were studied for single crystals of Ca_1−xGd_xF_2+x (x=1×10⁻⁴, 1×10⁻³, 1×10⁻² and 1×10⁻¹) and of Ca_0.8R_0.2F_2.2 (R=La, Ce, Pr, Nd, Gd, Dy, Er, Tm, Yb, Lu and Y), having the fluorite structure. The conductivity plots for the concentrated Ca_0.8R_0.2F_2.2 solid solutions display the low-temperature and high-temperature linear (Arrhenius) regions with the knee temperature T_k∼770 K. The values of the conductivity activation enthalpy obey the relation ΔH_HT(T>T_k)>ΔH_LT(T<T_k). The conductivity mechanism in heavily doped Ca_1−xR_xF_2+x crystals is associated with the clusters of the point defects which decrease the potential barriers for fluoride anions moving by hops over the structural sites of the anion sub-lattice. We studied the effect of the dimensional factor (doped cation radii) on the anionic transport in these crystals. A correlation between anionic transport and atomic structure of the studied crystals is discussed.     

Phonons in disordered solids

The effects of crystalline disorder on the frequency distribution and lifetimes of phonons are investigated. As the disorder parameter g characterizing the scattering of normal modes is increased to g>g_c, the normal mode spectrum becomes unstable against arbitrarily small nonlinearities while the ground state (if any) becomes increasingly degenerate. The bandwidth of the acoustic phonon spectrum increases with g, from a value ω_Dat g = 0 to 1.24ω_D at g_c. The speed of sound at long wavelengths decreases with increasing g; at threshold (g_c) it has decreased by some 29.3% from its value at g = 0. For g < g_c the scattering lifetime of long-wavelength normal modes satisfies Rayleigh's law (1/τ = A(_g)ω⁴). At g_c the damping satisfies a different law: 1/τ = Bω². Similar effects are obtained for the optic mode phonons. For these reasons, it appears that g_c marks the threshold of amorphous behavior, although the regime g >g_c is beyond the scope of our model.     

QCD sum rule determination of the axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, g_A(T). We find that g_A(T) is essentially independent of T, in the very wide range 0≤T≤0.9 T_c, where T_c is the critical temperature. While g_A at T=0 is q²-independent, it develops a q² dependence at finite temperature. We then obtain the mean square radius associated with g_A and find that it diverges at T=T_c, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.     

A-B site-bond correlated percolation for antiferromagnetic Ising model: The Bethe cluster approximation

We study the site-bond percolation problem for clusters of holes and particles with antiferromagnetic order by means of the Bethe cluster approximation. We find that the droplets (i.e.P _B =1?e ^?|K|/2) diverge at the antiferromagnetic critical pointH=0,T=T _c; however forH≠0 they diverge along a percolation line which is different from the Antiferromagnetic Phase Boundary except atT=0.     

Connections between thermodynamic quantities and vacancy and diffusion characteristics in binary metallic solid solutions

With the use of the similarity of interatomic potentials relations concerning vacancy and diffusion characteristics in disordered regular solid solutions have been derived. It has been shown that the vacancy concentration is constant along ifT_c(x) = T_A + (T_B ? T_A)x + 2ΔT_x(1?x), (T_A and T_B are the melting points of pure components A and B respectively, and ΔT is proportional to the excess enthalpy of mixing, x is the concentration of the atoms B) which is proportional to the binding energy of the crystal. The validity conditions of several empirical rules known in the literature are also analyzed. It has been found that the generalization of the well-known rule for self- and impurity diffusion in pure metals has the following form In $\text{D}{}_0{}^{\mathrm{z}}\text{(x) ～ p}\text{Q}{}^{\mathrm{z}}\text{(x)}\text{T}{}_{\mathrm{c}}\text{(x)}$ (Z = AorB) where p is a constant for alloys having identical structures (D₀^z(x) and Q^z(x) denote the preexponential factors and the activation energies respectively). The results calculated from the relations derived were compared with experimental data for tracer diffusion in the systems AgAu, CuNi (having slight deviation from regularity), Pb-Tl (showing ordering phenomena) and AlZn (clustering effects) and a good agreement was found.     

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).     

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A₁(x)T at doping levels x below the critical value x _c ^h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x _c ^h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A₁(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.