Influence of quantum fluctuations on the Néel temperature of a dilute two-dimensional anisotropic antiferromagnet

A quantum Monte Carlo procedure is used to calculate the energy, sublattice magnetization, Néel temperature, and the slopes of the S=[1/T _N(x=0)]dT _N(x)/dx curves as functions of the hole concentration and the exchange anisotropy Δ=1−J _x,y/J _z in the Heisenberg model with anisotropic negative interactions between nearest neighbors in a square lattice with dilution among the lattice sites. The slope diverges in the limit Δ→0: S∼ln(6.5/Δ). Fiz. Tverd. Tela (St. Petersburg) 39, 898–900 (May 1997)     

One-dimensional DLR invariant measures are regular

A system of infinite spins in one dimension is considered. The interaction is given by a pair potential –J _xyS_xS_y, whereS _x,S _y are the spins at the sitesx,y andJ _xy=J(|x–y|) whereJ(|x–y|) decreases asymptotically in an integrable way. The self-interaction makes the system superstable. It is proven that any invariant DLR measure for this system satisfies Ruelle's superstable estimates (regularity condition).     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Weak exchange interactions in the heteronuclear crystal CuPr2(CCl3COO)8·6H2O

The new heteronuclear crystal CuPr₂(CCl₃COO)₈·6H₂O, constructed of chains containing copper and praseodymium atoms, has been synthesized and investigated by EPR at 9.3 GHz at temperatures ranging from room temperature down to 10 K. At temperatures T∼300–130 K, EPR spectra are observed which are characteristic of isolated polyhedra of copper ions with g _z=2.330±0.005, g _x,y =2.053±0.005, A _z=139×10⁻⁴ cm⁻¹, and A _x,y <26×10⁻⁴ cm⁻¹. At temperatures T<130 K a complex spectrum is observed, associated with the appearance of weak exchange interactions between the copper ions in the chain (J _Cu-CuΣS _i·S _i+1), comparable in magnitude with the hyperfine interactions J _Cu-Cu=0.015 cm⁻¹ at T=10 K. The magnitude of the exchange interaction decreases smoothly as the temperature is raised. It is conjectured that orbitals of the praseodymium ions participate in the process of indirect exchange between the copper ions. Fiz. Tverd. Tela (St. Petersburg) 41, 2154–2157 (December 1999)     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

Stochastic dynamics in a two-level model of disorder: comparison of mean-field and exact solutions

Stochastic dynamics in the presence of quenched disorder (e.g., diffusion in a random medium) is generally treated in a suitable mean-field or effective medium approximation. While numerical simulations may help determine the accuracy of such approximations in specific models, there are relatively few instances in which analytic solutions are possible, to enable a precise comparison to be made with the mean-field results. We consider in this paper a simple but general model of quenched disorder in which a system variablex jumps stochastically between two valuesx _a andx _b . However, in each level there occurs with a certain probability a branch (or internal) state into which the system may fall, and from which a jump to the other level is possible only after a return to the original (or ‘active’) state. Four different configurations of the states of the system are thus possible, and the transitions between the states are governed by Markovian transition probabilities. The moments ofx and its autocorrelation function are computed in each case, and then configuration-averaged over the four realizations. This represents the exact solution. Next, a mean-field theory of the dynamics is developed: this turns out to involve an effective waiting-time density at each of the two levels that is non-exponential in time, so that the mean-field dynamics is a non-Markovian alternating renewal process. The moments and autocorrelation ofx are again computed, and compared with the exact solutions. The extent of the differences at both short and long times is elucidated, and a numerical comparison is presented for the case of maximal disorder.     

Ising models with two- and three-spin interactions: Mean field equation of state

The Ising model with pair and triplet interactions on the triangular lattice is solved in the mean-field approximation. With a sufficiently strong triplet interaction two first-order transitions take place at low temperature, and at intermediate temperatures one transition, terminating in a critical point. For J₂ > 0.75J₃ only the latter transition remains.     

Superconductivity, Seebeck coefficient, and band structure transformation in Y1−x CaxBa2Cu3−x CoxOy (x=0–0.3)

The temperature dependences of the resistivity and of the Seebeck coefficient S is studied in three series of Y_1−x Ca_xBa₂Cu_3−x Co_xO_y samples (x=0–0.3) differing in oxygen content. It was found that the critical temperature decreases for y≈7.0, and S(T=300 K) increases with doping, whereas oxygen deficiency results in a nonmonotonic variation of these quantities with increasing x. The band structure parameters have been determined from an analysis of the S(T) relations using a phenomenological theory of electron transport. It was found that an increase in x results in a gradual increase in band asymmetry, which is caused by calcium-induced creation of additional states in the band responsible for conduction in the normal phase. An analysis has shown that high impurity concentrations in oxygen-deficient Y_1−x Ca_xBa₂Cu_3−x Co_xO_y samples bring about an additional ordering of the structure, which may be caused by formation of a cobalt superlattice. It has also been shown that, in the case of Ca and Co codoping, the dependence of critical temperature on effective conduction-band width coincides with the universal correlation relation observed in the YBa₂Cu₃O_y system with single substitutions in various lattice sites. Fiz. Tverd. Tela (St. Petersburg) 41, 1363–1371 (August 1999)     

Formation of multilayer strained-layer heterostructures by liquid epitaxy. II. Simulation of the fabrication of heterostructures based on indium-arsenic-antimony-bismuth solid solutions

The formation of InAs_1−x−y Sb_xBi_y/InSb and InAs_1−x−y Sb_xBi_y/InSb_yBi_y strained-layer heterostructures by “capillary” LPE is simulated. The laws governing the dependence of the gap width E _g and the thickness d of the epilayers on the conditions of the process are revealed. It is shown that because of the sharp increase in the rate of epitaxial deposition as the LPE temperature is raised, the successful growth of epilayers of subcritical thickness is possible only up to T<550 K. The influence of the rate of laminar flow of the liquid in the growth channel in a relaxation regime and in a continuous pumping regime on the uniformity of the distribution of E _g and d in the epitaxial heterostructures is analyzed. Effective combinations of parameters for carrying out the process, which ensure the achievement of E _g ≈0.1 eV (77 K) in the active layers with variable-band-gap layers of minimal thickness, are established. Zh. Tekh. Fiz. 67, 50–56 (July 1997)     

Phase diagrams of (d x 2−y 2+id xy) superconductors on a square lattice

A model of strongly coupled electrons on a square lattice with attraction of the electrons to nearest-neighbor and next-nearest neighbor lattice sites is studied. For this model, the phase diagrams containing d _x ²−y ², d _xy, and (d _x ²−y ²+id _xy) states are constructed in the variables temperature versus chemical potential for different ratios of the corresponding potentials. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 356–360 (10 March 1998)     

Fluctuation-Induced Conductivity of Polycrystalline (Ho–Ce)Ba2Cu3O$_{7-\boldsymbol\delta}$ Superconductor

We report on systematic conductivity fluctuation measurements on samples of Ho_1 − x Ce _x Ba₂Cu₃O_7 − δ with x = 0.00, 0.05, and 0.10. The samples were produced by a standard solid-state reaction method, and the microstructure was analyzed by X-ray diffraction. To identify power-law divergences of the conductivity, the results were analyzed in terms of the temperature derivative of the resistivity dρ/dT and with the logarithmic derivative of the conductivity with respect to temperature − dln (Δσ)/dT. It was observed that the critical temperature decreases and that the transition width increases with increasing Ce doping. The data showed the occurrence of a two-stage transition besides the pairing transition splitting, associated with Ce doping and related with the occurrence of a phase separation. Above the critical temperature, the Gaussian and critical regimes were observed. On approaching the zero resistance state, our results showed a power-law behavior that corresponds to a phase transition from a paracoherent to a coherent state of the granular array.     

Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds

 We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice ℤ ^d . Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean- field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on ℤ ^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q≥3, the r-component cubic models with r≥4 and the O(N)-nematic liquid-crystal models with N≥3. Received: 22 July 2002 / Accepted: 12 January 2003 Published online: 5 May 2003 RID="⋆" ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted without charge. Communicated by J. Z.Imbrie     

Magnetic and structural phase transitions in the shape-memory ferromagnetic alloys Ni2+x Mn1−x Ga

The results of an experimental investigation of the temperature dependences of the magnetic susceptibility and resistivity in the shape-memory ferromagnetic alloys Ni_2+x Mn_1−x Ga (x=0–0.20) are reported. A T−x phase diagram is constructed on the basis of these data. It is shown that partial substitution of Ni for Mn causes the temperatures of the structural (martensitic) T _M and magnetic T _C (Curie point) phase transitions to converge. In the region where T _C =T _M the transition temperature increases linearly with magnetic field in the range from 0 to 10 kOe. The kinetics of a magnetic-field-induced martensitic phase transition is investigated, and the velocities of the martensite-austenite interphase boundary during direct and reverse transitions are measured. A theoretical model is proposed and the T−x phase diagram is calculated. It is shown that there exist concentration ranges where the magnetic and martensitic transitions merge into a first-order phase transition. The theoretical results are in qualitative agreement with experiment. Zh. éksp. Teor. Fiz. 115, 1740–1755 (May 1999)     

Synthesis and characterization of ZnxHg1?xSeyS1?y quantum dots

This article describes the synthesis of highly water-soluble Zn _x Hg_1−x Se _y S_1−y quantum dots (QDs) in aqueous solution through a simple photo-assisted reaction between ZnSe QDs and mercury(I) nitrate dihydrate [Hg₂(NO₃)₂·2H₂O]. In order to deduce the optimal synthesis conditions, we varied several parameters, including the concentrations of mercaptosuccinic acid (MSA) and Hg₂(NO₃)₂·2H₂O, the illumination time, and the reaction temperature. When irradiated at temperatures below 80 °C, the ZnSe QDs reacted with the S²⁻ ions formed rapidly from MSA and the Hg²⁺ ions formed from Hg₂ ²⁺ ions to form Zn _x Hg_1−x Se _y S_1−y QDs through a process of photo-etching and surface combination. Under different conditions, we prepared a series of Zn _x Hg_1−x Se _y S_1−y QDs that emit fluorescence at the maximum wavelengths ranging from 405 to 760 nm. Inductively coupled plasma-mass spectrometry and transmission electron microscopy/energy dispersive spectrometry revealed that the content of Hg in the Zn _x Hg_1−x Se _y S_1−y QDs was greater when the synthesis was conducted at higher temperature. The Zn_0.88Hg_0.12Se_0.44S_0.56 QDs exhibit improved photostability than crude ZnSe QDs and possess long lifetimes (τ₁ ~ 38 ns and τ₂ ~ 158 ns).     

Raman scattering in YBa2Cu3O7 single crystals: Anisotropy in normal and superconductivity states

Precise temperature and polarization dependences of Raman spectra have been investigated for fully oxygenated twin-free YBa₂Cu₃O₇ single crystals. We have found a striking superconductivity-induced x−y anisotropy in the temperature behavior of the 340 cm⁻¹ line: the magnitudes of the softening and broadening are quite different in the xx-and yy-polarizations. This anisotropy suggests a contribution of the CuO-chain superconductivity with a pairing symmetry different from that for the CuO₂ plane, or indicates that the superconducting gap amplitudes are different in the k _x and k _y directions. The d+s gap symmetry is the only realistic symmetry in the case of Δ_x≠Δ_y. Fiz. Tverd. Tela (St. Petersburg) 40, 403–412 (March 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Effect of interlayer single-particle hoppings on the superconducting transition temperature

It is well known that the superconducting transition temperature of high-T _c cuprates depends on the number of CuO₂ planes in the unit cell. The multilayer structure implies the possibility of interlayer hopping. Under the assumption that the interlayer hopping can be specified by the parameter t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))², the quasiparticle excitation spectrum for the bilayer cuprate in the superconducting state has been determined in the framework of the t − t′ − t″ − t _⊥ − J* model using the generalized mean-field approximation. It turns out that the interlayer hoppings does not create any additional mechanism of the Cooper paring and does not lead to an increase in T _c . The splitting of the upper Hubbard quasiparticle band attributed to the interlayer hoppings is manifested as two peaks in the doping dependence of the superconducting transition temperature at temperatures below the maximum T _c value for a single-layer cuprate. It has been found that antiferromagnetic interlayer correlations suppress the interlayer splitting. This probably leads to the common doping dependence of T _c for both single-layer and bilayer cuprates.     

First-Order Phase Transition in Potts Models with Finite-Range Interactions

We consider the Q-state Potts model on Z ^d , Q≥ 3, d≥ 2, with Kac ferromagnetic interactions and scaling parameter γ. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for γ small enough there is a value of the temperature at which coexist Q+1 Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for d = 2, Q = 3, in contrast with the case of nearest-neighbor interactions for which available results indicate a second order phase transition. Putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction.     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Metastates in disordered mean-field models: Random field and hopfield models

We rigorously investigate the size dependence of disordered mean-field models with finite local spin space in terms of metastates. Thereby we provide an illustration of the framework of metastates for systems of randomly competing Gibbs measures. In particular we consider the thermodynamic limit of the empirical metastate , whereμ _n (η) is the Gibbs measure in the finite volume {1,…,n} and the frozen disorder variableη is fixed. We treat explicitly the Hopfield model with finitely many patterns and the Curie-Weiss random field Ising model. In both examples in the phase transition regime the empirical metastate is dispersed for largeN. Moreover, it does not converge for a.e.η, but rather in distribution, for whose limits we given explicit expressions. We also discuss another notion of metastates, due to Aizenman and Wehr.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.