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.     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

Collapse transition of a two-dimensional lattice animal

The phase diagram and the tricritical point of a collapsing lattice animal are studied through an extended series expansion of the isothermal compressibilityK _T on a square lattice. As a function of the variables of fugacity and Boltzmann weight,K _T is investigated using partial differential approximant techniques. The characteristic flow pattern of partial differential approximant trajectories is determined for a stable fixed point. We obtain satisfactory estimates for the tricritical fugacityx _t =0.024±0.005 and temperatureT _t =0.54±0.04. Taking into account only linear scaling fields, we are also able to get the scaling exponent =1.4±0.2 and the crossover =0.66±0.08. Our results are in reasonable agreement with previous estimates in the literature.     

Temperature dependence of the Raman bandwidths and intensities of a lattice mode near the tricritical and second order phase transitions in NH4Cl

We calculate here the temperature dependence of the damping constant using the expressions derived from the Matsushita's theory and the temperature dependence of the order parameter from the molecular field theory for the tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. Our calculations are performed for the ν ₅ (174?cm^?1) Raman mode of NH₄Cl for the pressures studied. Predictions for the damping constant are in good agreement with our observed Raman bandwidths of this lattice mode for both pressures. The Raman intensities calculated from the molecular field theory by means of the order parameter are also in good agreement with our observed Raman intensities of the ν ₅ (174?cm^?1) mode for both tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. In this study our observed Raman intensities of this lattice mode are analysed using a power-law formula with the critical exponent β for the order parameter at those two pressures considered in NH₄Cl. From our analysis, the value of β?=?0.5 is obtained as the mean field value.     

Collapse of two-dimensional linear polymers

We study the collapse transition of a two-dimensional, very long polymer. The model we consider is a lattice model where the chain is represented by a self-avoiding walk with nearest-neighbor attraction. By using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width. We then use finite-size scaling to determine the values of the tricritical ( point) exponentsv ₁=0.55±0.01v _u=1.15±0.15 ₁/v₁=1.80±0.05 We compare these results to the other values already proposed in the literature.     

The statistical mechanics of spin-1 Ising model with AFM/AFM interactions on a bilayer Bethe lattice

The spin-1 Ising model is studied for the case of antiferromagnetic (AFM)/AFM interactions on the bilayer Bethe lattice by using the pairwise approach for several values of the coordination numbers q=3, 4 and 6 when the layers are linked with the external magnetic fields. The ground state (GS) phase diagrams, thermal variations of the order-parameters and the response functions are studied in detail to obtain the phase diagrams of the model. It was found that the system gives only one Néel temperature, T_N, for q=3. Two T_N's and first-order phase transition temperature, T_t, thus tricritical point, are found and the existence of two T_N's leads to the reentrant behavior when q=4 and 6 for some given system parameters.     

Mixed-Spin Ising Model in an Oscillating Magnetic Field and Compensation Temperature

Godoy et al. (Phys. Rev. B 69, 054428, 2004) presented a study of the magnetic properties of a mixed spin (1/2,1), Ising ferrimagnetic model on a hexagonal lattice without an oscillating magnetic field. They employed dynamic mean-field calculations and Monte Carlo simulations to find the compensation point of the model and to present the phase diagrams. It has been found that the N-type compensation temperature appears only when the intrasublattice interaction between spins in the σ sublattice is ferromagnetic. Moreover, the system only undergoes a second-order phase transition. In this work, we extend the study a dynamic compensation temperature of a mixed spin-1/2 and spin-1 Ising ferrimagnetic system on a hexagonal lattice in the presence of oscillating magnetic field within the framework of dynamic mean-field calculations. We find that the system displays the N-type compensation temperature. We also calculate dynamic phase diagrams in which contain the paramagnetic, ferrimagnetic, nonmagnetic fundamental phases and two different mixed phases, depending on the interaction parameters and oscillating magnetic field. The system also exhibits tricritical and reentrant behaviors.     

The application of the differential operator method to the Blume-Emery-Griffiths model

Within an effective-field approximation, general expressions for evaluating the second-order phase transition line and the tricritical point of the anisotropic Blume-Emery-Griffiths model are obtained by the use of the differential operator technique. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice (z = 3) and square lattice (z = 4). We find a new disordered phase which may correspond to the staggered quadrupolar phase predicted in the Monte Carlo simulation, when some conditions are satisfied. The phase diagrams for z = 3 and z = 4 systems exhibit a reentrant behavior for positive values of the uniaxial anisotropy parameter. The change of the tricritical point with the value of the reduced biquadratic parameter is also studied for the system with z = 3.     

Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point

We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffiths model [Phys. Rev. A 4 (1971) 1071–1077]. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters n, β, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling limits and 18 MDPs for the total spin. These limit results are obtained as (β,K) converges along appropriate sequences (β_n, kn) to points belonging to various subsets of the phase diagram, which include a curve of second-order points and a tricritical point. The forms of the limiting densities in the scaling limits and of the rate functions in the MDPs reflect the influence of one or more sets that lie in neighborhoods of the critical points and the tricritical point. Of all the scaling limits, the structure of those near the tricritical point is by far the most complex, exhibiting new types of critical behavior when observed in a limit-theorem phase diagram in the space of the two parameters that parametrize the scaling limits. American Mathematical Society 2000 Subject Classifications. Primary 60F10, 60F05, Secondary 82B20     

Selection of Species in Divalent Rhodium Hexacyanide Using Pulsed EPR

The superposition of paramagnetic species in CW EPR spectra usually prevents the measurement of spectral parameters. Separation of superimposed species can be performed in field-swept pulsed EPR by choosing a convenient pulse sequence in such a way that species with different relaxation times can be distinctly affected. Computer subtraction between spectra taken under different conditions may lead to better species identification. ForT₂-based selection, the difference between FID-detected and long τ echo-detected spectra is used. This technique is successfully applied to the [Rh(CN)₆]⁴⁻paramagnetic species created by radiation damage in [Rh(CN)₆]³⁻in a KCl host lattice, where spectra corresponding to different positions of a charge-compensating positive-ion vacancy are superimposed.     

Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.     

The McMillan parameter as an effective field variable for the nematic–smectic tricritical point in NO.M compounds

The dependence of the coupling of orientational and translational order parameters on the nematic-smectic A tricritical point (TCP), observed through birefringence experiments in the pure compounds and in the binary mixtures in the homologous series of N(p-n-alkyloxybenzylidene)p-n-alkylanilines, results in a mean field tricritical exponent. The McMillan parameter, M = T _NA/T _NI (where T _NA and T _NI are the smectic A—nematic (AN) and the nematic—isotropic (NI) phase transition temperatures respectively), is used as an effective and relevant field variable in analysing the TCP. The observed linear dependence of the jump in the orientational order parameter with new density variables in the tricritical region is found to be consistent with the results obtained from both the Landau mean field and the decoupled mean field models. The width of the mean field tricritical region is discussed in terms of the McMillan parameter. Further, the McMillan parameter is observed to be characteristic of chemical composition at the NA tricritical point.     

Trimers of bivalent copper impurity ions in CaF<Subscript>2</Subscript> crystals: The structure and mechanism of formation

Crystals of CaF₂: Cu (with a copper impurity content higher than 0.1 at. %) grown by the Czochralski method from a melt in a mixed helium-fluorine atmosphere are investigated using electron paramagnetic resonance (EPR) spectroscopy. It is found that the crystals contain paramagnetic centers whose magnetic properties at low temperatures are identical to those of [CuF₄F₄]^6? (S=1/2) single centers. The magnetic properties of the centers exhibit a qualitative change in the temperature range 77–300 K. These changes are described within a model according to which the center is treated as a cluster composed of three [CuF₄F₄]^6? impurity complexes involved in exchange interactions and interactions occurring in the field of Jahn-Teller lattice distortions.     

The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

Critical behavior of a mixed ferrimagnetic ternary alloy on the Bethe lattice

The critical behavior of the mixed Ising model of the type AB _p C_1−p ternary alloy consisting of spins σ = 1/2, S = 1, and m = 3/2 is investigated on the Bethe lattice by using the exact recursion relations. The exact expressions for the magnetizations and magnetic susceptibilities are found, and the thermal behaviors of the magnetizations and susceptibilities are studied. The magnetizations and susceptibilities have also been investigated as functions of the crystal-field interaction or single-ion anisotropy. The phase diagram has been constructed according to which the system always undergoes a second-order phase transition for the coordination number q ≤ 3 and second-and first-order phase transitions for q > 3; hence, the system has a tricritical point. The system also exhibits reentrant behaviors. The text was submitted by the authors in English.     

Specific heat and latent heat of KMnF3 ferroelastic crystal

The specific heat and the heat flux exchanged by a single crystal of KMnF₃ have been measured simultaneously while cooling the sample at constant rate of 0·06 K/h through the phase transition at T ₀= 186 K. The phase transition is weakly first order and close to a tricritical point. The temperature dependence at T185 K of the excess specific heat and the excess entropy follow very well the predictions of a Landau potential at a tricritical point.     

Monte Carlo study of tricritical dynamics in two dimensions

The dynamical tricritical behavior for the spin-1 Ising model with single-ion interaction is investigated in two dimensions using Monte Carlo simulations. The nonlinear dynamical tricritical exponentz _t is determined from the asymptotic power-law relaxation of the magnetization. The valuez _t = 1.99 ± 0.04 reported here is the first estimate of the dynamical exponent at a multicritical point, in two dimensions.On leave from Departamento de Fisica, Universidade Federal de Pernambuco, Recife-PE, Brazil.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond _F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d _F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.     

Thermoelectric power and magnetic properties of Cu doped NiZn ferrite for technological application

A series of samples in the system Ni_0.65Zn_0.35Cu_xFe_2-xO₄ (x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5) were prepared by the usual ceramic technique. The thermoelectric power and the magnetic susceptibility were measured. The transition from the ferrimagnetic to the paramagnetic state is accompanied by an increase in the thermo EMF. NiZn ferrite shows n-type conductivity due to the presence of Fe²⁺ ions. The addition of Cu²⁺ ions creates lattice vacancies which give rise to p-type conductivity.

The Tawfik coefficient was determined for NiZn ferrite in the paramagnetic state. This coefficient was reduced by addition of Cu up to x < 0.5.