The effect of a surface on the dynamic and thermodynamic properties of S=1 Heisenberg ferromagnet with biquadratic exchange

Properties of semi-infinite (S=1) Heisenberg ferromagnet with biquadratic exchange were studied in terms of surface exchange (=I_S/I) and biquadratic coupling (a). It was shown that a strict correlation exists, depending on , between the type of surface spin waves (acoustic or optical) and the mean-field (MF) critical temperature, bulk (T_c) and surface T_c^S>T_c (for ). Within the framework of the Landau–Ginsburg theory for semi-infinite simple cubic ferromagnet, a detailed study is presented of the critical behaviour of the system, in particular in the vicinity of the tricritical point which is the consequence of the biquadratic interaction. It is shown that tricritical exponents satisfy exactly the scaling relations for d=3. The analysis of the spin–spin correlation function within the framework of the same theory, shows that there occurs the critical magnetic scattering of low-energy electrons (LEED) from the surface in the case , when the ordering temperature T_c^S is approached from above (from paramagnetic phase). In the opposite case, , there occurs no surface critical scattering. It was also shown that in the vicinity of the tricritical point, the biquadratic interaction increases the range of validity of the MF approximation.     

In-plane magnetoresistance of electron-doped superconducting thin films Pr0.9LaCe0.1CuO4

We measured the in-plane magnetoresistance of Pr_0.9LaCe_0.1CuO₄ (PLCCO) epitaxial thin films under various magnetic fields H applied parallel to the tetragonal c-axis. The measurements were performed at the superconducting state as well as the normal state. As the magnetic field is between the low critical field H_c1 and upper critical field H_c2, a critical scaling behavior of electrical resistivity is found. We analyze the electrical transport properties and show the magnetic field H dependence of glass transition temperature T_g and the characteristic temperature T^* for the PLCCO film, which may shed some light on vortex behavior in electron-doped superconductors.     

Trap-size scaling of finite Bose systems within an exact canonical ensemble

Based on an exact canonical partition function, we investigate the trap-size scaling for ideal Bose gases with a finite number of particles N confined in a cubic box or in a harmonic trap. We study the trap-size scaling behaviors of condensate fraction 〈n₀〉/N and specific heat C_N around the transition temperature T_c (i.e., t = T/T_c − 1 → 0) for the three different traps, where a trap exponent θ in dependence of the trapping potential and the universality class of transition are introduced. In the box trap with periodic and Dirichlet boundary conditions, where θ → 1, we find that the scaling functions governing the various critical behaviors are universal but respective of the boundary conditions. The calculated critical exponents are in nice agreement with analytical scaling predictions. The borders of universality validity are obtained numerically. In the case of the harmonic trap, the critical behavior of the system is also found to be universal, and the trap exponent is obtained as θ ? 0.068.     

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     

Critical absorption in binary liquid systems

The refractive index of coexisting phases in two binary liquid systems, viz., perfluorodekalineheptane (PFD-H) and acetic anhydride-pentane (AA-P), in the vicinity of the critical consolution temperature of the system T _c was measured. It was shown that it is possible to observe (using the refractometry method, if the instrument is updated appropriately) critical absorption phenomena; a surface layer enriched by perfluorodekaline (in the PFD-H system) and by pentane (in the AA-P system) occurs at the liquid-vapor interface near the critical consolute point under T > T _c .     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Richtungseffekte der Lichtausbeute von Anthrazen bei Beschü\ mit Protonen im Energiebereich 200–600 keV

The results of the three-dimensional liquid droplet model are compared with experiment and other phenomenological theories. The homogeneity assumption of the scaling laws holds both above and belowT _c , and various series expansions can be derived. But there is a nonanalyticity near the critical isotherm aboveT _c for fixed “field” μ?μ(p _c ,T); and liquid and gas are not symmetric about the critical isochore aboveT _c . Both results contradict the usual scaling assumptions and experiment. The equation of state is fixed if the density on the coexistence curve and the critical pressure are known. Therefore we can derive various relations between critical quantities. They are compared with experiment and the corresponding relations in the Vicentini-Missoni ansatz, the parametric representation, and the generalized Landau ansatz. The disagreement ranges from about 20% to one order of magnitude.     

Ullah-Dorsey Scaling of Fluctuation Conductivity Near the Superconducting Transition in (LaSe)1.14(NbSe2)

Magnetotransport measurements with the quasi two-dimensional misfit-layer compound (LaSe)_1.14(NbSe₂) with critical temperature T _c = 1.23 K are presented. The temperature dependence of the upper critical magnetic field H _c2 has been determined from an analysis of magnetoresistance data through the scaling procedure obtained theroretically by Ullah and Dorsey for the fluctuation conductivity. We show that in contrast to a direct determination of H _c2(T) with a positive curvature the temperature dependence of H _c2 obtained via the scaling procedure reveals a negative curvature in agreement with the Werthammer-Helfand-Hohenberg theory for conventional type-II superconductors.     

Light scattering and small angle neutron scattering experiments with an aggregating binary liquid mixture of critical composition

Results of light scattering and small angle neutron scattering experiments with a 2-butoxyethanol (2-C₄E₁)/D₂O mixture of critical composition (stoichiometric mole fraction of 2-C₄E₁x = 0.0598; critical temperature T_c (visual) = 42.714 °C) are reported. They are carried out with the aim to find out whether the temperature dependence of the correlation length ξ characterizing the extension of concentration fluctuations near T_c is different from that characterizing the size of aggregates of the 2-C₄E₁ molecules which appear to exist at temperatures away from T_c. The experiments show that the temperature dependence of ξ near T_c is the same as that away from T_c within the uncertainty of the measurements. – As a by-product of this study, neutron scattering data were collected corresponding to a wide range of values of the scaling variable x (3 < x < 2100; x = qξ q is the absolute value of the scattering vector). They are analysed in terms of the limiting form of the universal correlation scaling function gξ(x) = C₁x^?(2-η) to determine the value of the universal critical exponent η. A value of η = 0.039 ± 0.004 is found. It is considered consistent with the theoretically expected values.     

Nonlinear scaling and its application to ferromagnetic systems

Making use of renormalization-group ideas, a scaling equation of state applicable to ferromagnetic systems and involving the nonlinear scaling variables =ε/t and =h/t, instead of the usual linear scaling variables ε=(T-T_c)/Tc = t-1 and h=H (ordering field), has been derived. The magnetic equation of state so obtained is then generalized to take into account the effect of nonlinear relevant and irrelevant scaling fields. To facilitate a comparison with experiments, the analytic (non-analytic) corrections to the dominant singular behaviour of spontaneous magnetization (order parameter) M(T, 0), ‘zero-field’ susceptibility χ(T, 0), and specific heat in zero field that the nonlinear relevant (irrelevant) scaling fields give rise to are explicitly calculated up to third order in Due consideration is also given to the modifications in the Arrott-Noakes form of the scaling equation of state and the Kouvel-Fisher definition of the effective susceptibility exponent brought about by these scaling fields. A detailed analysis of the M(T, 0) and χ(T, 0) data for crystalline and amorphous ferromagnets in terms of the theoretical expressions derived in this work reveals that i) in conformity with the theoretical predictions, the “;non-analytic”; corrections to the singular behaviour dominate over the “;analytic”; ones for temperatures in the immediate vicinity of the critical point Tc, whereas reverse is the case for temperatures far away from Tc and (ii) the expression for χ(T, 0), based on the nonlinear scaling arguments, which includes the leading “;analytic”; correction, reproduces closely the observed variation of χ with T over a wide range of temperatures T_c ≤ T ≤ 1.5T_c (in some cases, up to 3T_c) for both ordered as well as quench-disordered ferromagnets.     

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T _c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T _c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T _c ⁽¹⁾ and T _c , which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T = 0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.     

On the high temperature staggered susceptibility of Heisenberg model antiferromagnetics

The critical ordering temperature, T _c′, for the antiferromagnetic Heisenberg model is investigated on the basis of the high temperature expansion for the staggered susceptibility. For the simple cubic and body-centred cubic lattices, it appears that

where q is the lattice coordination number, S the spin value and T _c the corre-sponding ferromagnetic Curie point. A possible counter argument asserting T _c′ ? T _c is discussed at some length.     

Trivial, Critical and Near-critical Scaling Limits of?Two-dimensional Percolation

It is natural to expect that there are only three possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of the plane are surrounded by arbitrarily large loops and every deterministic point is almost surely surrounded by a countably infinite family of nested loops with radii going to zero, and (3) an intermediate one, in which every deterministic point of the plane is almost surely surrounded by a largest loop and by a countably infinite family of nested loops with radii going to zero. We show how one can prove this using elementary arguments, with the help of known scaling relations for percolation. The trivial limit corresponds to subcritical and supercritical percolation, as well as to the case when the density p approaches the critical probability, p _c , sufficiently slowly as the lattice spacing is sent to zero. The second type corresponds to critical percolation and to a faster approach of p to p _c . The third, or near-critical, type of limit corresponds to an intermediate speed of approach of p to p _c . The fact that in the near-critical case a deterministic point is a.s. surrounded by a largest loop demonstrates the persistence of a macroscopic correlation length in the scaling limit and the absence of scale invariance.     

Scaling functions for critical surface scattering

Scattering of x-rays at grazing angles is studied for semi-infinite systems which exhibit a second order phase transition. We calculate the scaling functions for the diffuse scattering intensity aboveT _c and for the Bragg-intensity belowT _c, using -expansion techniques. Corrections to the leading critical surface behaviour and the size of the asymptotic scaling region are discussed. In addition, we obtain the crossover function for the excess susceptibility _s.This work was supported by Bundesministerium für Forschung und Technologie     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Critical behavior of electrical resistivity in amorphous Fe-Zr alloys

Electrical resistivity (ρ) of the amorphous (a-)Fe_100−c Zr _c (c=8.5, 9.5 and 10) alloys has been measured in the temperature range 77 to 300 K, which embraces the second-order magnetic phase transition at the Curie temperature point T _c. Analysis of the resistivity data particularly in the critical region reveals that these systems have a much wider range of critical region compared to other crystalline ferromagnetic materials. The value of T _c and specific heat critical exponent, α has the same values as those determined from our earlier magnetic measurements. The value of α for all the present investigated alloys are in close agreement with the values predicted for three-dimensional (3D) Heisenberg ferromagnet systems, which gives contradiction to the earlier results on similar alloys. It is observed from the analysis that the presence of quenched disorder does not have any influence on critical behavior.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.