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 diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. 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 η=1/2, i.e.T=0 is thus a critical point.     

Nonequilibrium phase transition in stochastic lattice gases: Simulation of a three-dimensional system

We report results of computer simulations of a three-dimensional lattice gas of interacting particles subject to a uniform external fieldE. The dynamics of the system is given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction ofE. As for the two-dimensional system we find that here too there exists a critical temperature,T _c (E) such that forT < T _c (E) the systems orders in a very anisotropic phase with striplike typical configurations parallel to the field.T _c (E) increases withE but substantially less strongly than in two dimensions. There is a break in the slope of the saturation current atT _c (E). Our data are consistent with the critical exponent being mean field.     

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     

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.     

High-quality YBCO d.c. SQUIDs based on bicrystal substrates

Summary An analysis of superconducting transport properties and magnetic behaviour of d.c. SQUIDs employing YBCO bicrystal grain boundary junctions (GBJs) has been performed. GBJs have been obtained by deposition of ac-axis-oriented YBCO film on a SrTiO₃ bicrystal substrate by ICM sputtering technique. Experimental measurements on a YBCO d.c. SQUID with a misorientation angle θ=20° are reported. The SQUID shows a critical temperatureT _c∼89 K and a high critical current densityJ _c∼3·10⁶ A/cm² atT=4.2 K. Current-voltage characteristics are close to the behaviour predicted by the resistively shunted junction (RSJ) model and the temperature dependenceJ _c(T) shows a linear behaviour at small reduced temperatures and a depressedJ _c value close toT _c. High-quality flux-voltage curves have been found upT=87 K over a large range of magnetic field. The high reproducibility and the good control of transport properties by the variation of θ make YBCO bicrystal GBJs very useful for applications in electronics. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Zum Kondo-Effekt in Zink-Mangan: Der Einfluß der Manganverteilung auf den elektrischen Widerstand im Temperaturbereich bis 0,4 °K

The electrical resistivity of dilute Zn-Mn alloys (c=0–0.6 at% Mn) has been measured in a temperature range from room temperature (RT) down to 0.4 °K. Three different series of samples are investigated: 1. annealed 72 h, 400 °C, 2. annealed and aged 1 year atRT, 3. coldworked atRT. All samples show a minimum in the residual resistance atT _min∝c ^1/5 followed by an increase of the resistivityρ∝k _s · lnT (Kondo-effect). For some alloys the resistivity minimum is followed by a resistivity maximum atT _max.T _max mainly depends on the distribution of the Mnatoms in the Zn-matrix. The coefficientk _s is also strongly influenced by changes of the Mn-distribution. For alloys withc>0.02 at% (max. solubility of Mn in Zn atRT) the slopek _s =?ρ/? lnT decreases with increasing degree of precipitation of the manganese. Samples withc<0.02 at% however, show the opposite effect, increasingk _s with increasing Mn-precipitation. Moreover, during the aging process, we observe an increase in the “residual resistance” (resistance ratioR _T/R ₂₉₃ atT _min) for these alloys. The effect can be explained by assuming that the precipitation leads to the formation of superparamagnetic clusters.     

Critical dynamics and stability of elastically coupled systems at marginal dimensionalities

Static and dynamic behavior of an-component classical model atd=4 has been investigated assuming a coupling to a fluctuating lattice displacement field. Solutions of renormalization-group (RG) equations are given for elastically isotropic and anisotropic systems, and the temperature dependences of elastic constants and of the corresponding damping coefficients are calculated. For isotropic and weakly anisotropic systems it is found that forn<4 the critical regime can be split into a rigid regimet>t _s , and a compressible regimet<t _s , wheret=(T–T _c )/T _c andt _s is a crossover temperature. In the rigid regime, the logarithmic correction factors characterizing deviations from Landau theory have the same form as in systems without elastic coupling; in the compressible regime the exponents are renormalized by the coupling. Forn4 rigid behavior prevails at all temperatures; similarly only rigid behavior is found for strongly anisotropic systems for alln. The thermodynamic stability of the system is investigated by evaluating the contribution of ring diagrams for the casen=1. It is thus shown that under constant hydrostatic pressure a first-order transition occurs in both isotropic and anisotropic systems, and the corresponding equations for the transition temperature and the value of the order parameter atT _c are derived.     

Magnetic relaxation spectra of YbPd2Si2

We present the results of inelastic neutron scattering experiments on the intermediate-valent system YbPd₂Si₂ to investigate the magnetic relaxation behaviour. We have performed measurements on polycrystalline samples with neutrons of incident energyE ₀=3.1 meV at temperatures between 1.5 K and 250 K, and withE ₀=12.7 meV andE ₀=50.8 meV at temperatures between 5 K and 50 K using time-of-flight spectrometers. At temperaturesT>50 K we find a pure quasielastic magnetic response with a rather broad linewidth typical for intermediate-valent systems. AtT50 K an inelastic excitation line appears at about 21 meV; its intensity increases with decreasing temperature. In the same temperature range (T<50 K) the quasielastic linewidth decreases rapidly and atT=5 K the quasielastic response has been apparently transformed to a second inelastic feature at about 4.7 meV. The width of this low-energy excitation fits well to the temperature dependence of the quasielastic linewidth forT>5 K.     

Phase diagram of the two-dimensional Ising antiferromagnet (computer-assisted proof)

We study the phase diagram of the Ising antiferromagnet on a square lattice in a neighbourhood of ground state critical pointsh=±4,T=0. It leads to a question about the valuea _c of the critical activity of the hard-square lattice gas. Using a constructive criterion of uniqueness we prove thata _c >1 and that the phase diagram of the antiferromagnet does not bulge near mentioned critical points. It is a specific feature of this work that the proof was completed with the help of a computer.     

Superconductivity and magnetic order in CaLaBaCu3O z

X-ray diffraction, thermogravimetric analysis, magnetization and Mossbauer studies of a⁵⁷Fe probe, in CaLaBa(Cu_1−x Fe _x )₃O _z withz=7, 6.5 andx=0.00 to 0.05 have been performed. Forz=7,T _c drops from 74 K forx=0.00 to 35 K forx=0.05. In CaLaBa(Cu_1−x Fe _x )₃O _z withz=7, 10% of the iron is magnetically ordered withH _eff=530 K kOe andT _N=400 K, even though the sample is superconducting. In the oxygen poor, non-superconducting samples (z=6.5) 20% of the iron is magnetically ordered withH _eff=340 kOe andT _N=340 K. Since the iron reflects the magnetic order of the Cu(2) ions, this may show that perhaps two inequivalent Cu(2) sites exist in CaLaBa(Cu_1−x Fe _x )₃O₇, ones of which is magnetically ordered. The experimental observations may be interpreted in terms of the special crystal structure which can allow superconductivity and magnetism to coexist, probably in separate Cu(2) planes.     

Phase diagram for three-dimensional correlated site-bond percolation

The Coniglio-Stanley-Klein model is a random bond percolation process between the occupied sites of a lattice gas in thermal equilibrium. Our Monte Carlo simulation for 40³ and 60³ simple cubic lattices determines at which bond thresholdp _Bc , as a function of temperatureT and concentrationx of occupied sites, an infinite network of active bonds connects occupied sites. The curvesp _Bc (x, T) depend only slightly onT whereas they cross over if plotted as a function of the field conjugate tox. Except close toT _c we find 1/p _Bc to be approximated well by a linear function ofx, in the whole interval between the thresholdx _c (T) of interacting site percolation atp _Bc =1 and the random bond percolation limitx=1 atp _Bc =0.248±0.001. Thisx _c (T) varied between 0.22 forT=0.96 (coexistence curve) and 0.3117±0.0003 forT= (random site percolation). At the critical point (T=T andx=1/2) we confirmed quite accurately the predictionp _Bc =1-exp(–2J/k _B T _c ) of Coniglio and Klein. As a byproduct we found 0.89±0.01 for the critical exponent of the correlation length in random percolation.     

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).     

Critical behavior of short range Potts glasses

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form exp(const.T ^–2), and an algebraic singularity atT0.25 ind=4. We conclude that the lower critical dimension of the present model isd _c =3 or very close to it. Some of the critical exponents are estimated and their respective values discussed.     

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.     

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.     

The speed of sound in hadronic matter

We calculate the speed of sound c _s in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)～m ^?a exp?{bm}, which leads to singular behavior at the critical temperature T _c =1/b. With a=4 the pressure and the energy density remain finite at T _c , while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near T _c resonance effects dominate, which causes c _s to vanish as (T _c ?T)^1/4. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around T _c , the actual critical behavior in these models is no longer present.     

High magnetic field study of sulphur spinel Cu1/2In1/2Cr2S4

High magnetic field measurements indicate that a first order transition occurs in Cu_1/2In_1/2Cr₂S₄ atT<35 K along aH _c (T) line in a (H, T) phase diagram. This confirms previous calorimetric and neutron diffraction experiments. It is suggested that this set of experimental results may be explained by a transition from long range to spin-glass magnetic ordering related to the frustration existing on the underlying fcc Bravais lattice obtained by grouping four by four ferromagnetically coupled spins on top of a tetrahedron.     

Statistical interpretation of the inclusive muon pair production parameters

An approach is developed which allows us to interpret in statistical terms the quantities involved in the expression,a(1–x_F) ^c exp (–b.P _T) which is used for parameterization of the high energy inclusive muon pair production. In particular, withs being the number of sorts of constituents (partons, quarks),x _F=1–1/s and [b.(P _T)₀]s 1 whereb. (P _T)₀ is the dimensionless slope and (P _T)₀ fixes the scale of the transverse momentum; furthermore, the parameterc itself determines the number of elementary creations of the constituents under investigation. The validity of that statistical interpretation for other production phenomena is discussed as well.Talk given at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

Nucleon propagator at finite temperature

We study the nucleon propagator at finite temperature in the framework of finite energy QCD sum rules. We find that the nucleon mass is approximately constant over a wide range of temperature, increasing sharply near the critical temperature for deconfinementT _c . The coupling of the nucleon to quarks is a monotonically decreasing function ofT, vanishing atT=T _c .     

Temperature-dependent electronic structure of gadolinium

We investigate the electronic structure of the ferromagnetic 4f-metal Gadolinium by use of a many-body evaluation of a generalized model of magnetism, the one-particle part of which is derived from an ASW-LSDA bandstructure calculation. A striking temperature-dependence of the conduction band states is traced back to a 4f-(5d, 6s) interband exchange. The conduction electron polarization (0.63 _B atT=0) decreases forTT _c very similar to the 4f-magnetization. A red shift of the lower -band edge of about 0.25 eV appears upon cooling fromT=T _c toT=0. — The quasiparticle band-structure exibits a remarkable non uniform magnetic behaviour at different positions in the Brillouin zone, and in particular for different subbands. Weakly correlated (s-like) dispersions show a Stoner-likeT-dependence of the exchange splitting. On the other hand, stronger correlated (d-like) dispersions split belowT _c into four branches, two for each spin direction. TheirT-dependence mainly concerns the spectral weights of the quasiparticle peaks and not so much the energetic positions. An exchange caused splitting remains even forT<T _c .