Yukio Okwamoto

Incommensurate-Commensurate Crossover in Generalized One-Dimensional Ginzburg-Landau Field. II

Effects of the commensurability energy on the fluctuating incommensurate state in one-dimensional systems are investigated exactly by means of the transfer integral method on the basis of the generalized Ginzburg-Landau model. At low temperatures the fundamental eigenvalue equation of the method is solved by expanding it in powers of the temperature in analogy with the ordinary WKB method. Our analytic results on the low temperature behavior of the correlation length can be interpreted in terms of phasons and discommensurations. At intermediate temperatures various physical quantities are calculated numerically. In particular from the temperature dependence of the correlation length we determine the crossover point from the fluctuating incommensurate state to the commensurate state.

Incommensurate-Commensurate Transition in Two-Dimensional Sine-Gordon System

The two-dimensional classical sine-Gordon system which contains a misfit parameter µ in one direction is investigated at a particular temperature. This model at that temperature is transformed into a one-dimensional free spinless Fermi system. The commensurate phase is stable when µ is smaller than the critical value µ c . The fluctuating incommensurate state is realized when µ>µ c . The mean misfit near the critical value µ c behaves as (µ-µ c ) 1/2 . The Fourier transform of the correlation function is also calculated. In the incommensurate phase it has a delta-function and a logarithmically divergent term in addition to a broad peak. Its behavior can be understood in terms of the fluctuating discommensurations.

Ground-State Energy and Gap of Alternating Antiferromagnetic Linear Chains

Alternation rarameter δ dependences of the ground-state energy (GE) e (δ) and the gap Δ (δ) in the excitation spectrum of the spin Hamiltonian H = J ∑ l =1 N [1+(-1) l δ] [ S l x S l +1 x + S l y S l +1 y +σ S l z S l +1 z ] are calculated in two numerical methods, with interest in the exponents β of the GE and α of the gap which are defined as e (δ) - e (0)∝δ β and Δ (δ)∝δ α for small δ. First by means of the 2-level renormalization group calculation the exponents are obtained as β∼1.78 and α∼0.96 for the isotropic Heisenberg model (σ=1). Second by means of the finite chain extrapolation, β for σ=1 is obtained as 1.68 -0.36 +0.13 from the data of the extrapolated GE between δ=0.05 and 0.1.

Phase Diagram of a Two-Dimensional Heisenberg Antiferromagnet in a Magnetic Field

An analytical study is made on a two-dimensional classical isotropic Heisenberg antiferromagnet in a uniform magnetic field. This model is expected to show the Kosterlitz-Thouless phase transition due to a XY-like degeneracy of a canted spin-flop ground state. It is shown that the transition temperature approaches zero logarithmically as the field approaches zero.

Coexistence of Reconstructed Surface Phases of H/W(001)

The W(001) surface with adsorbed hydrogen is studied at low coverages near the reconstruction transition temperature on the basis of the theoretical model proposed by Lau and Ying. It is shown in the mean field approximation that a narrow coexistence region appears between the two reconstructed surface phases at the directional switching transition (c(2×2) →c(2×2) ). An effect of thermal fluctuation is qualitatively discussed.

Two-Dimensional Sine-Gordon Lattice with Fixed Winding Number: A Molecular-Dynamics Study

With the use of molecular-dynamics technique, the power spectra of displacements have been calculated for the two-dimensional sine-Gordon lattice with fixed winding number at thermal equilibrium. A gap has been clearly observed in the excitation spectra at sufficiently low temperatures. With increasing temperature the finite spectra are found at the frequencies in the gap. These observed data are analyzed with the temperature-dependent spectra of domain-wall oscillations and optical phonons.

Thermodynamic Properties of Anisotropic Two-Dimensional Sine-Gordon Lattice: Molecular-Dynamics Calculations

By the use of molecular dynamics technique, we studied the thermodynamic properties of the anisotropic two-dimensional (2D) sine-Gordon lattice. Anisotropy parameter γ is introduced as the ratio of the strength of stretching to that of shear coupling. Energy-temperature curves are caleulated with varying γ. We found that the peak temperature of specific heat changes with γ. These observed thermodynamic propertics are analyzed in the case of 1D and nearly isotropic 2D system.

Equivalence of Two Types of Singlet Wave Functions for the Triangular Lattice Antiferromagnet

A one-body problem on the triangular lattice is solved in the presence of a fictitious magnetic field which produces a quarter of a flux quantum through each triangle. Then it is shown explicitly that the fractional quantum Hall wave function for a ground state of the s =1/2 triangular lattice antiferromagnet is equivalent to a variational singlet wave function written by a pair of determinants which are made out of eigenfunctions of the one-body problem.

The Thirring Model at a Finite Fermion Density

The spectrum of the massless Thirring model at a finite fermion density is examined, using the Bethe ansatz, with the momentum cutoff. The cutoff procedure in this letter is valid for the model within the first order of the coupling constant.

Molecular-Dynamics Calculations of Two-Dimensional Sine-Gordon Lattice

We have performed the molecular-dynamics calculations for the two-dimensional sine-Gordon lattice and obtained the internal energies and the time correlation functions of displacements. The experimental results at low temperatures are in good agreement with the analysis in terms of the self-consistent phonon approximation.