Asymptotics of the susceptibility for the Ising model on the hierarchical lattices

Using the GKS inequality Griffiths and Kaufman showed in [12] that the susceptibility in the Ising model on the hierarchical lattices is infinite forT>T _c . In the present work we give an analytic calculation of the dominant singularity of the susceptibility whenh0 forT>T _c . Moreover we analytically find the spontaneous magnetization forT<T _c and prove that forT<T _c the susceptibility is finite.     

Three-dimensional Gross-Neveu model at nonzero temperature and in the presence of an external electromagnetic field

The phase structure of the (2+1)-dimensional Gross-Neveu model is considered at a nonzero temperatureT and in the presence of an external electromagnetic field. The major results are as follows: 1. AtT=0,H0 (a magnetic field), the original symmetry of the model breaks for anyH values. 2. AtT=0,E0 (an electric field) anE _c is shown to exist, such that forEE _c the original symmetry is broken, but forE>E _c the vacuum of the model is symmetric. 3. AtT0,H0, and at a fixedT value such anH _c (T) is shown to exist that forH>H _c (T) the chiral invariance of the model is spontancously broken. For any fixedH value there exists such anT _c (H) that forT>T _c (H) the symmetry restores. The phase portrait of the model is drawn.     

On the continuity of the magnetization and energy in Ising ferromagnets

We investigate the phase diagram of ferromagnetic Ising spin systems satisfying the G.H.S. inequality. We show that they cannot have a normal first-order phase transition as the temperatureT is varied, i.e., one where the magnetization is discontinuous and there are three coexisting phases. Furthermore, for n.n. interactions, discontinuity in the magnetization at 0 <T ₀ T _c implies an uncountable infinity of pure phases atT ₀.     

Extremity of the disordered phase in the Ising model on the Bethe lattice

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme forTT _c ^SG , whereT _c ^SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme forT _c ^SG .     

Disordered spherical model

The most general expression of the free energy in the disordered spherical model is obtained. Based on this expression the following are shown, (a) The ferromagnetic order in the translationally invariant spherical model is unstable against an arbitrarily small random field ifd 4. (b) Straightforward generalization of the spherical model to the disordered case for a finite-range interaction has some rather unnatural properties: the phase transition in the model exists even in one dimension, and even in the case of ferromagnetic interaction it does not vanish as a homogeneous external field is switched on and spontaneous magnetization is zero forT _c . (c) For the ferromagnetic interaction, a modification of the disordered spherical model is proposed which does not have such properties and displays the behavior expected for the disordered ferromagnets. The paper also discusses the role of fluctuation (cluster) effects and the structure of the spontaneous magnetization field for the disordered spherical model. The results essentially rest upon the spectral properties of random self-adjoint operators obtained by the author earlier and in the present paper.     

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.     

Influence of the ground state of the Pr<Superscript>3+</Superscript> ion on magnetic and magnetoelectric properties of the PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe₃(BO₃)₄ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below T _N = 32 K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial (l ∥ c), while, in a strong magnetic field H ∥ c (H _cr ～ 43 kOe at T = 4.2 K), a Fe³⁺ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an H-T phase diagram. The contribution of the Pr³⁺ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.     

Quantenstatistik eines Gases mit verschiedener Bahn- und Spintemperatur

A system of particles with spin in a magnetic field may possess an orbital temperatureT _o different from the spin temperatureT _s (?0), if it is possible to neglect the energetic interaction between the orbital and the spin system. The calculation of the quantum statistical most probable distribution of identical independent particles on the orbital and spin energy levels yields the introduction of three Lagrange multipliers—according to the fact that the orbital and the spin energy and the number of particles are fixed—representing the orbital and spin temperature and a generalizedPlanck's “characteristic function”. Apart from the Boltzmann-approximation being valid in the case of small spin values forT _o ?T _e (T _e =customary degeneration temperature) and arbitraryT _s ?0, the distributions and the orbital and the spin energy depend onboth the temperaturesT _o andT _s coming from the principle of exclusion forFermi resp.Bose particles. The equations of state are discussed. There are four heat capacities, which possess characteristic peaks. In stead of the well-known temperature independence of the paramagnetism of degenerated conducting electrons one obtains χ～T _o /T _s . The behaviour of the Einstein-condensation of aBose gas is considered.     

T c =0-Ordering in the ruby Ising-spin glass?

Isothermal and adiabatic susceptibilities characterize the rubies under investigation, (Cr _x Al_1–x )₂O₃ with 0.00025x0.008, as symmetric Ising spin glasses with a rms interaction of . Spin-freezing phenomena, like cusps, plateaus, and thermoremanence in the low-field magnetization are associated with a restricted heat transfer between the spin system and the thermal bath in the precritical region (TJ). At equilibrium andTJ, the scaling of the non-linear magnetization and the slowing down of the zerofield, average relaxation rate indicate a spin glass transition atT _c =0. Among possible reasons for this apparent discrepancy to theT _c J-hypothesis by Ogielski et al., are internal random fields.     

Analyticity of correlation functions for the two-dimensional Ising model

Analyticity of correlation functions for the two-dimensional Ising model as a function of the inverse temperature except for the singularity at the critical temperature is proved. A crucial step is the establishment of the correspondence between extremal equilibrium states of the model and pure ground states of a one-dimensional spin system below the critical temperatureT _c . An exact decay rate of the clustering property along axes is also determined for allTT _c .     

Aging effects in the nonequilibrium behavior of multilayer magnetic superstructures

A numerical Monte Carlo study of the nonequilibrium behavior of multilayer magnetic superstructures consisting of alternating magnetic and nonmagnetic nanolayers is performed. The calculated two-time autocorrelation function and the staggered magnetization of the structure at its evolution starting from various initial states are analyzed. The analysis reveals aging effects characterized by a slowing down of the relaxation and correlation characteristics in the system with the waiting time. It is shown that, in contrast to bulk magnetic systems, the aging effects in magnetic superstructures arise not only near the ferromagnetic ordering temperature T _c in the films but also within a wide temperature range at T ≤ T _c.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

On the Measurement of the Stiffness of Spin Waves in the Fe<Subscript>0.75</Subscript>Co<Subscript>0.25</Subscript>Si Helimagnet by the Small-Angle Neutron Scattering Method

The stiffness of spin waves in the Fe_0.75Co_0.25Si helimagnet with the Dzyaloshinskii–Moriya interaction in a state fully magnetized by an external field has been measured by the small-angle neutron scattering method. It has been shown that the dispersion of magnons in this state is anisotropic because the neutron scattering pattern consists of two circles for neutrons with obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field H and equal to the wave vector of the spiral ±k_s measured in inverse nanometers. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnitude of the magnetic field. It has been shown that the stiffness of spin waves A for the helimagnet is equal to 46.0 meV Ų at T = 0 K and decreases weakly (by 20%) with increasing temperature up to the critical value T_c = 38 K.     

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.     

Magnetic order in Sr x Ca1−x Cu0.99 57Fe0.01O2

Sr _x Ca_1–x Cu_0.99 ⁵⁷Fe_0.01O₂ was studied forx=0.13, 0.15, and 0.17. Mössbauer spectroscopy and magnetization measurements indicate magnetic ordering characteristic of spin glass systems withT _f70K forx=0.15 and 0.13.     

Ferromagnetism in the thermodynamically stable monolayer Fe(110) on W(110), coated by Ag

Ferromagnetic order in the thermodynamically stable, pseudomorphic monolayer Fe(110) on W(110), coated by Ag, was studied in situ in UHV using Conversion Electron Mössbauer Spectroscopy (CEMS) and Torsion Oscillation Magnetometry (TOM). Films near the monolayer coverage, prepared at 475 K, consist of nearly independent monolayer and double-layer patches. The properties of monolayer patches are nearly independent of the mean film thickness resulting in excellent conditions to determine the true monolayer properties. The Curie temperature is reduced toT _{c, mono}= 282 K = 0.27 T_c,bulk, the ground state hyperfine field is reduced toB _hf(0)=11.9 T = 0.35B _hf,bulk(0) and the magnetic moment per atom is enhanced to(0) = 2.53 _B=1.14(0)_bulk. Remanent magnetization is detected forT 260 K=0.92T _{c, mono}, square loop magnetization forT 230 K=0.82T _{c, mono}. Unusual properties of the phase transition are detected by the combination of both experimental techniques.     

μSR studies of YFeMnO4

Muon spin relaxation (SR) studies were carried out on YFeMnO₄. Two interesting phenomena were found in measurements of longitudinal relaxation time spectra atT>T _cusp for a single crystal: (1) difference of the relaxation rates between the directions parallel with and perpendicular to thec-axis, and (2) suppression of local field fluctuations in a longitudinal external field. The spectra atT >T _cusp were reproduced with the function exp[-(₀ t)]. The results are discussed under a picture of the magnetic spin fluctuations of triangular antiferromagnets.     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

On a classical spin glass model

A simple, exactly soluble, model of a spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, but its solution can be obtained without replicas. As the temperatureT is lowered, the spin-glass phase is reached via an equilibrium phase transition atT=T _f . The spin-glass magnetization exhibits a distinctS-shape character, which is indicative of a field-induced transition to a state of higher magnetization above a certain threshold field. For suitable probability distributions of the exchange interactions.

1. A mixed phase is found where spin-glass and ferromagnetism coexist.
2. The zero-field susceptibility has a flat plateau for 0≦T≦T _f and a Curie-Weiss behaviour forT>T _f .
3. At low temperatures the magnetic specific heat is linearly dependent on the temperature.

The physical origin of the dependence upon the probability distributions is explained, and a careful analysis of the ground state structure is given.