arXiv subjects

A. A. Katanin

Publications and source records attributed to A. A. Katanin.

102 records · Page 6Linked to original sources

arXiv2001

Effects of the Van Hove singularities on magnetism and superconductivity in the t-t' Hubbard model: a parquet approach

The t-t' Hubbard model for the Fermi level near the Van Hove singularity is considered within the renormalization group and parquet approaches. The interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.

cond-mat.str-el↗

arXiv2000

A supersymmetric mean-field approach to the infinite-U Hubbard model

A generalized supersymmetric representation of the Hubbard operator algebra is considered. This representation is applied to the infinite-U Hubbard model. A mean-field theory which takes into account both on-site and inter-site virtual boson-fermion transitions is developed. Unlike previous approaches, the mean-field theory considered is free from divergences. Possible application of these results to the ferromagnet-paramagnet transition, as well as to other problems is discussed.

cond-mat↗

arXiv2000

Quantitative Description of Thermodynamics of Layered Magnets in a Wide Temperature Region

The thermodynamics of layered antiferro- and ferromagnets with a weak interlayer coupling and/or easy-axis anisotropy is investigated. A crossover from an isotropic 2D-like to 3D Heisenberg (or 2D Ising) regime is discussed within the renormalization group (RG) analysis. Analytical results for the the (sublattice) magnetization and the ordering temperature are derived are obtained in different regimes. Numerical calculations on the base of the equations obtained yield a good agreement with experimental data on La2CuO4 and layered perovskites. Corresponding results for the Kosterlitz-Thouless and Curie (Néel) temperatures in the case of the easy-plane anisotropy are derived.

cond-mat.str-el↗

arXiv1999

Calculation of Neel temperature for S=1/2 quasi-one-dimensional Heisenberg antiferromagnets

Isotropic S=1/2 quasi-one-dimensional antiferromagnets are considered within the bosonization method. The 1/zp-corrections to the interchain mean-field theory (zp is the number of nearest neighbors in transverse to chain directions) are obtained for the ground-state sublattice magnetization and Neel temperature T_N. The corrections to T_N make up about 25% of mean-feld value, while those to ground-state sublattice magnetization are small enough (especially in the three-dimensional case). The fluctuation corrections obtained improve considerably the agreement with the experimental data for magnetic-chain compounds KCuF3, Sr2CuO3 and Ca2CuO3.

cond-mat↗

arXiv1999

Orientational phase transitions in anisotropic rare-earth magnets at low temperatures

Orientational phase transitions are investigated within the Heisenberg model with single-site anisotropy. The temperature dependence of the cone angle is calculated within the spin-wave theory. The role of the quantum renormalizations of anisotropy constants is discussed. A comparison with the experimental data on the cone-plane orientational transition in holmium is performed.

cond-mat↗

arXiv1999

On the self-consistent spin-wave theory of layered Heisenberg magnets

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional (2D) Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the non-linear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.

cond-mat.str-el↗

arXiv1998

The Kosterlitz-Thouless and magnetic transition temperatures in layered magnets with a weak easy-plane anisotropy

The two-dimensional (2D) Heisenberg magnet with a weak easy-plane anisotropy is considered. A renormalization group (RG) analysis in this model is performed for both quantum and classical cases. A crossover from the Heisenberg to 2D XY model is discussed. The magnetic transition owing to the interlayer coupling is considered. Analytical results for the Kosterlitz-Thouless and Curie (Neel) temperatures are derived with account of two-loop corrections. The results are compared with experimental data, e.g. on K2CuF4, and turn out to provide a quantitative description, unlike the standard one-loop results.

cond-mat↗

arXiv1998

Quantum phase transitions and thermodynamic properties in highly anisotropic magnets

The systems exhibiting quantum phase transitions (QPT) are investigated within the Ising model in the transverse field and Heisenberg model with easy-plane single-site anisotropy. Near QPT a correspondence between parameters of these models and of quantum phi^4 model is established. A scaling analysis is performed for the ground-state properties. The influence of the external longitudinal magnetic field on the ground-state properties is investigated, and the corresponding magnetic susceptibility is calculated. Finite-temperature properties are considered with the use of the scaling analysis for the effective classical model proposed by Sachdev. Analytical results for the ordering temperature and temperature dependences of the magnetization and energy gap are obtained in the case of a small ground-state moment. The forms of dependences of observable quantities on the bare splitting (or magnetic field) and renormalized splitting turn out to be different. A comparison with numerical calculations and experimental data on systems demonstrating magnetic and structural transitions (e.g., into singlet state) is performed.

cond-mat↗

arXiv1997

Thermodynamics of isotropic and anisotropic layered magnets: renormalization group approach and 1/N expansion

The O(N) model of layered antiferro- and ferromagnets with a weak interlayer coupling and/or easy-axis anisotropy is considered. A renormalization group (RG) analysis in this model is performed, the results for N=3 being expected to agree with those of the 1/M expansion in the CP^{M-1} model at M=2. The quantum and classical cases are considered. A crossover from an isotropic 2D-like to 3D Heisenberg (or 2D Ising) regime is investigated within the 1/N expansion. Analytical results for the temperature dependence of the (sublattice) magnetization are obtained in different regimes. The RG results for the ordering temperature are derived. In the quantum case they coincide with the corresponding results of the 1/N expansion. The numerical calculations on the base of the equations obtained yield a good agreement with experimental data on the layered perovskites La2CuO4, K2NiF4 and Rb2NiF4, and the Monte Carlo results for the anisotropic classical systems.

cond-mat↗

arXiv1997

1/N Expansion for Critical Exponents of Magnetic Phase Transitions in CP^{N-1} Model at 2<d<4

Critical exponents in the CP^{N-1} model, which describes localized-moment ferro- and antiferromagnets (N=2 in the Heisenberg model), are calculated from two-particle Green's functions to first order in 1/N. For d=2+εthe results agree with earlier renormalization group calculations. For d=3 the leading 1/N-corrections turn out to be very large at N=2. For d=4-εthe 1/N-corrections are small at any N and insufficient to describe correctly the magnetic phase transition.

cond-mat↗

arXiv1997

Critical behavior and the Neel temperature of quantum quasi-two-dimensional Heisenberg antiferromagnets

The nonlinear sigma-model and its generalization on N-component spins, the O(N) model, are considered to describe thermodynamics of a quantum quasi-two-dimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Neel temperature and spin correlation function are calculated to first order of the 1/N-expansion. A description of crossover from a 2D-like to 3D regime of sublattice magnetization temperature dependence is obtained. The values of the critical exponents derived are β=0.36, η=0.09. An account of the corrections to the standard logarithmic term of the spin-wave theory modifies considerably the value of the Neel temperature. The thermodynamic quantities calculated are universal functions of the renormalized interlayer coupling parameter. The renormalization of interlayer coupling parameter turns out to be considerably temperature dependent. A good agreement with experimental data on La2CuO4 is obtained. The application of the approach used to the case of a ferromagnet is discussed.

cond-mat↗

arXiv1997

On the Self-Consistent Spin-Wave Theory of Two-Dimensional Magnets With Impurities

The self-consistent spin-wave theory is applied to investigate the magnetization distribution around the impurity in isotropic and easy-axis two-dimensional ferro- and antiferromagents. The temperature dependences of host magnetization disturbance and impurity magnetization are calculated. The short-range order in the isotropic case is investigated. Importance of dynamic and kinematic interactions of spin waves is demonstrated.

cond-mat↗