arXiv subjects

Doochul Kim

Publications and source records attributed to Doochul Kim.

27 records · Page 2Linked to original sources

arXiv1997

Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.

cond-mat.stat-mech↗

arXiv1997

Effect of Anisotropy on the Localization in a Bifractal System

Bifractal is a highly anisotropic structure where planar fractals are stacked to form a 3-dimensional lattice. The localization lengths along fractal structure for the Anderson model defined on a bifractal are calculated. The critical disorder and the critical exponent of the localization lengths are obtained from the finite size scaling behavior. The numerical results are in a good agreement with previous results which have been obtained from the localization lengths along the perpendicular direction. This suggests that the anisotropy of the embedding lattice structure is irrelevant to the critical properties of the localization.

cond-mat.mes-hall↗

arXiv1996

Anisotropic Surface Growth Model in Disordered Media

We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of the nonlinear KPZ terms. It turns out that the surface height correlation functions in each direction scales distinctively. The anisotropic behavior is attributed to the asymmetric behavior of the quenched KPZ equation in 1+1 dimensions with respect to the sign of the nonlinear KPZ term.

cond-mat.stat-mech↗

arXiv1996

Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero vertical field. The energy gaps scale with size $N$ as $N^{-1/2}$ and its amplitudes are obtained in terms of level-dependent scaling functions. Exactly on the phase boundary, the amplitudes are proportional to a sum of square-root of integers and an anomaly term. By summing over all low-lying levels, the partition functions are obtained explicitly. Similar analysis is performed also at the phase boundary of zero horizontal field in which case the energy gaps scale as $N^{-2}$. The partition functions for this case are found to be that of a nonrelativistic free fermion system. From symmetry of the lattice model under $π/2$ rotation, several identities between the partition functions are found. The $N^{-1/2}$ scaling at zero vertical field is interpreted as a feature arising from viewing the Pokrovsky-Talapov transition with the space and time coordinates interchanged.

cond-mat.stat-mech↗

arXiv1995

Finite-size scaling and the toroidal partition function of the critical asymmetric six-vertex model

Finite-size corrections to the energy levels of the asymmetric six-vertex model transfer matrix are considered using the Bethe ansatz solution for the critical region. The non-universal complex anisotropy factor is related to the bulk susceptibilities. The universal Gaussian coupling constant $g$ is also related to the bulk susceptibilities as $g=2H^{-1/2}/π$, $H$ being the Hessian of the bulk free energy surface viewed as a function of the two fields. The modular covariant toroidal partition function is derived in the form of the modified Coulombic partition function which embodies the effect of incommensurability through two mismatch parameters. The effect of twisted boundary conditions is also considered.

cond-mat↗

arXiv1995

Bethe ansatz solution for crossover scaling functions of the asymmetric XXZ chain and the Karder--Parisi--Zhang-type growth model

A perturbative method is developed to calculate the finite size corrections of the low lying energies of the asymmetric XXZ hamiltonian near the stochastic line. The crossover from isotropic to anisotropic, Kardar-Parisi-Zhang (KPZ) scaling of the mass gaps is determined in terms of universal crossover scaling functions. At the stochastic line, the asymmetric XXZ hamiltonian describes the time evolution of the single-step or body-centered solid-on-solid growth model in one dimension. The mass gaps of the growth model are found as a function of the growth rate and the substrate slope. Higher order corrections to the growth model mass gaps are also calculated to obtain the first terms of the KPZ to Edward-Wilkinson crossover scaling function in the large argument expansion in the zero slope sector.

cond-mat↗

arXiv1994

Phase transitions in interacting domain-wall model

We investigate the interacting domain-wall model derived from the triangular-lattice antiferromagnetic Ising model with two next-nearest-neighbor interactions. The system has commensurate phases with a domain-wall density $q=2/3$ as well as that of $q=0$ when the interaction is repulsive. The $q=2/3$ commensurate phase is separated from the incommensurate phase through the Kosterlitz--Thouless~(KT) transition. The critical interaction strength and the nature of the KT phase transition are studied by the Monte Carlo simulations and numerical transfer-matrix calculations. For strongly attractive interaction, the system undergoes a first-order phase transition from the $q=0$ commensurate phase to the incommensurate phase with $q\neq 0$. The incommensurate phase is a critical phase which is in the Gaussian model universality class. The effective Gaussian coupling constant is calculated as a function of interaction parameters from the finite-size scaling of the transfer matrix spectra .

cond-mat↗

arXiv1993

Interacting Domain Walls and the Five-Vertex Model

We investigate the thermodynamic and critical properties of an interacting domain wall model which is derived from the triangular lattice antiferromagnetic Ising model with the anisotropic nearest and next nearest neighbor interactions. The model is equivalent to the general five--vertex model. Diagonalizing the transfer matrix exactly by the Bethe Ansatz method, we obtain the phase diagram displaying the commensurate and incommensurate (IC) phases separated by the Pokrovsky--Talapov transitions. The phase diagram exhibits commensurate phases where the domain wall density $q$ is locked at the values of $0$, $1/2$ and $1$. The IC phase is a critical state described by the Gaussian fixed point. The effective Gaussian coupling constant is obtained analytically and numerically for the IC phase using the finite size scaling predictions of the conformal field theory. It takes the value $1/2$ in the non-interacting limit and also at the boundaries of $q=0$ or $1$ phase and the value $2$ at the boundary of $q=1/2$ phase, while it varies smoothly throughout the IC region. (TO APPEAR IN PHY. REV. E)

cond-mat↗

arXiv1993

Honeycomb lattice solvable models

We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer matrices with different spectral parameters commute with each other. At the critical point, the finite-size scaling of the transfer matrix spectrum for the honeycomb lattice models is written in terms of the quantities obtained from the finite-size scaling of the square lattice solvable models. We study in detail the phase transition properties of two models based on the interacting hard square model and the magnetic hard square model, respectively. The models, in general, can be extended to the IRF version of the Z-invariant models of Baxter.

cond-mat↗