arXiv subjects

Hiromi Otsuka

Publications and source records attributed to Hiromi Otsuka.

At least 19 recordsLinked to original sources

arXiv2026

Berezinskii-Kosterlitz-Thouless phase transitions of the antiferromagnetic Ising model with ferromagnetic next-nearest-neighbor interactions on the kagome lattice

We investigate the six-state clock universality of the Ising model on the kagome lattice, considering antiferromagnetic nearest-neighbor (NN) and ferromagnetic next-nearest-neighbor (NNN) interactions. Our comprehensive study employs three approaches: the level-spectroscopy method, Monte Carlo simulations, and a machine-learning phase classification technique. In this system, we observe two Berezinskii-Kosterlitz-Thouless (BKT) transitions. We present a phase diagram consisting of three phases: the low-temperature ordered phase with sublattice magnetizations, the intermediate BKT phase, and the high-temperature disordered phase, as a function of the ratio of the NNN interaction to the NN interaction. We verify the six-state clock universality through the machine-learning study, which uses data from the six-state clock model on the kagome lattice for training.

cond-mat.stat-mech↗

arXiv2025

BKT transitions of the XY and six-state clock models on the various two-dimensional lattices

In a two-dimensional (2D) spin system, the XY model, characterized by planar rotational symmetry, exhibits a unique phenomenon known as the Berezinskii-Kosterlitz-Thouless (BKT) transition. In contrast, the clock model, which introduces discrete rotational symmetry, exhibits the BKT transition at two different temperatures due to this discreteness. In this study, we numerically investigate the BKT transition for XY and six-state clock models over various two-dimensional lattices. We employ two primary methods: the Monte Carlo method, which analyzes the size dependence of the ratio of the correlation functions for two different distances, and a machine-learning approach to classify the different phases -- namely, the low-temperature ordered phase, the intermediate BKT phase, and the high-temperature disordered phase. We identify the BKT transition temperatures for the XY and six-state models on honeycomb, kagome, and diced lattices. Combined with the previously calculated data for the triangular lattice, we then compare these values with the second-order phase transition temperatures of the 2D Ising model, for which exact solutions are known. Our results indicate that the ratio of the BKT transition temperatures for each lattice relative to the Ising model transition temperatures are close, although the values are not universal.

cond-mat.stat-mech↗

arXiv2023

Comprehensive studies on the universality of BKT transitions -- Machine-learning study, Monte Carlo simulation, and Level-spectroscopy method

Comprehensive studies are made on the six-state clock universality of two models using several approaches. We apply the machine-learning technique of phase classification to the antiferromagnetic (AF) three-state Potts model on the square lattice with ferromagnetic next-nearest-neighbor (NNN) coupling and the triangular AF Ising model with anisotropic NNN coupling to study two Berezinskii-Kosterlitz-Thouless transitions. We also use the Monte Carlo simulation paying attention to the ratio of correlation functions of different distances for these two models. The obtained results are compared with those of the previous studies using the level-spectroscopy method. We directly show the six-state clock universality for totally different systems with the machine-learning study.

cond-mat.stat-mech↗

arXiv2022

Universal asymptotic correlation functions for point group $\boldsymbol{C_{6v}}$ and an observation for triangular lattice $\boldsymbol{Q}$-state Potts model

We investigate universal forms for asymptotic correlation functions of off-critical systems that possess $C_{6v}$ symmetry following the argument for $C_{4v}$ symmetry in Phys.~Rev.~E{\bf 102},~032141. Unlike the $C_{4v}$ case, a minimal form exists that contains only two free parameters: the normalization constant and modulus. Using this form as a building block, we can construct next asymptotic forms to the minimal one. We perform large-scale Monte Carlo simulations of the triangular lattice $Q$-state Potts model above the transition temperature and successfully obtain numerical evidence to support a wide applicability of the minimal form to lattice models, including unsolvable ones. From the calculated minimal form, we derive the universal shape of equilibrium crystals in the honeycomb lattice Potts model described by an algebraic curve of genus 1. Although the curve differs from those obtained in the $C_{4v}$ case, the latters also have genus 1. We indicate that the birational equivalence concept can play an important role in comparing asymptotic forms for different point group symmetries, for example, $C_{6v}$ and $C_{4v}$.

cond-mat.stat-mech↗

arXiv2021

Large peaks in the entropy of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice in a [111] magnetic field

We study the residual entropy of the nearest-neighbor spin-ice model in a magnetic field along the [111] direction using the Wang-Landau Monte Carlo method, with a special attention to dilution effects. For a diluted model, we observe a stepwise decrease of the residual entropy as a function of the magnetic field, which is consistent with the finding of the five magnetization plateaus in a previous replica-exchange Monte Carlo study by Peretyatko {\it et al.} [Phys. Rev. B {\bf 95}, 144410 (2017)]. We find large peaks of the residual entropy due to the degeneracy at the crossover magnetic fields, $h_c/J$ = 0, 3, 6, 9, and 12, where $h$ and $J$ are the magnetic field and the exchange coupling, respectively. In addition, we also study the residual entropy of the diluted antiferromagnetic Ising models in a magnetic field on the kagome and triangular lattices. We again observe large peaks of the residual entropy, which are associated with multiple magnetization plateaus for the diluted model. Finally, we discuss the interplay of dilution and magnetic fields in terms of the residual entropy.

cond-mat.dis-nn↗

arXiv2021

Universal dynamics of magnetic monopoles in two-dimensional kagomé ice

A magnetic monopole in spin ice is a novel quasiparticle excitation in condensed matter physics, and we found that the ac frequency dependent magnetic susceptibility $χ(ω)$ in the two-dimensional (2D) spin ice (so-called kagomé ice) of Dy$_2$Ti$_2$O$_7$ shows a single scaling form. This behavior can be understood in terms of the dynamical scaling law for 2D Coulomb gas (CG) systems [Phys. Rev. B 90, 144428 (2014)], characterized by the charge correlation length $ξ(\propto1/\sqrt{ω_1})$, where $ω_{1}$ is a characteristic frequency proportional to the peak position of the imaginary part of $χ(ω)$. It is a generic behavior among a wide variety of models such as the vortex dynamics of 2D superconductors, 2D superfluids, classical XY magnets, and dynamics of melting of Wigner crystals.

cond-mat.other↗

arXiv2020

Asymptotic correlation functions in the $Q$-state Potts model: a universal form for point group $C_{4v}$

Reexamining algebraic curves found in the eight-vertex model, we propose an asymptotic form of the correlation functions for off-critical systems possessing rotational and mirror symmetries of the square lattice, i.e., the $C_{4v}$ symmetry. In comparison with the use of the Ornstein-Zernike form, it is efficient to investigate the correlation length with its directional dependence (or anisotropy). We investigate the $Q$-state Potts model on the square lattice. Monte Carlo (MC) simulations are performed using the infinite-size algorithm by Evertz and von der Linden. Fitting the MC data with the asymptotic form above the critical temperature, we reproduce the exact solution of the anisotropic correlation length (ACL) of the Ising model ($Q=2$) within a five-digit accuracy. For $Q=3$ and 4, we obtain numerical evidence that the asymptotic form is applicable to their correlation functions and the ACLs. Furthermore, we successfully apply it to the bond percolation problem which corresponds to the $Q\rightarrow1$ limit. From the calculated ACLs, the equilibrium crystal shapes (ECSs) are derived via duality and Wulff's construction. Regarding $Q$ as a continuous variable, we find that the ECS of the $Q$-state Potts model is essentially the same as those of the Ising models on the Union Jack and 4-8 lattices, which are represented in terms of a simple algebraic curve of genus~1.

cond-mat.stat-mech↗

arXiv2014

A cluster algorithm for Monte Carlo simulations of spin ice

We present an algorithm for Monte Carlo simulations of a nearest-neighbor spin ice model based on its cluster representation. To assess its performance, we estimate a relaxation time, and find that, in contrast to the Metropolis algorithm, our algorithm does not develop spin-freezing. Also, to demonstrate the efficiency, we calculate the spin and charge structure factors, and observe pinch points in a high-resolution color map. We then find that Debye screening works among defects and brings about short-range correlations, and that the deconfinement transition triggered by a fugacity of defects $z$ is dictated by a singular part of the free-energy density $f_{\rm s}\propto z$.

cond-mat.stat-mech↗

arXiv2013

AC Susceptibility of the Dipolar Spin Ice Dy2Ti2O7: Experiments and Monte Carlo Simulations

Experimental data of the frequency-dependent ac susceptibility for the dipolar spin ice Dy2Ti2O7 has been analyzed by Monte Carlo simulations on the basis of the single-spin-flip Metropolis algorithm. We have directly evaluated the ac susceptibility by applying an ac magnetic field. We found that the simulated behaviors reproduces the experimental behavior of the ac susceptibility in the temperature range from 0.6 to 1.0 K, where dilute magnetic monopoles diffusively move. The conversion factor from simulation time to real time, i.e., the rate of hopping of monopoles to nearest-neighbor sites, strongly depends on temperature.

cond-mat.str-el↗

arXiv2013

A Scaling Theory for ac Magnetic Response in Kagome Ice

A theory for frequency-dependent magnetic susceptibility χ(ω) is developed for thermally activated magnetic monopoles in kagome ice. By mapping this system to a two-dimensional (2D) Coulomb gas and then to a sine-Gordon model, we have shown that the susceptibility has a scaling form χ(ω)/χ(0)={\cal F}(ω/ω_1), where the characteristic ω_1 is related to a charge correlation length between diffusively moving monopoles, and to the sine-Gordon principal breather. The dynamical scaling is universal among superfluid and superconducting films, and 2D XY magnets above Kosterlitz-Thouless transitions.

cond-mat.str-el↗

arXiv2011

Monomer-Dimer Mixture on a Honeycomb Lattice

We study a monomer-dimer mixture defined on a honeycomb lattice as a toy model for the spin ice system in a magnetic field. In a low-doping region of monomers, the effective description of this system is given by the dual sine-Gordon model. In intermediate- and strong-doping regions, the Potts lattice gas theory can be employed. Synthesizing these results, we construct a renormalization-group flow diagram, which includes the stable and unstable fixed points corresponding to ${\cal M}_5$ and ${\cal M}_6$ in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.

cond-mat.stat-mech↗

arXiv2009

Classical dimer model with anisotropic interactions on the square lattice

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a two-fold ``zero-energy flat band'' in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.

cond-mat.stat-mech↗

arXiv2008

Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach

We investigate infinite-order phase transitions like the Berezinskii-Kosterlitz-Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the operator-production-expansion technique, we perform the renormalization-group analysis, and then clarify properties of marginal operators near the phase transition points. The results are utilized to establish criteria to determine the transition points and some universal relations among excitation levels to characterize the transitions. We verify these predictions via the numerical analysis on eigenvalue structures of the transfer matrix. Also, we discuss an enhancement of symmetry at the end points of a critical intermediate phase in connection with a transition observed in the ground state of the bilinear-biquadratic spin-1 chain.

cond-mat.stat-mech↗

arXiv2008

Finite-size-scaling ansatz for the helicity modulus of the triangular-lattice three-spin interaction model

The Berezinskii-Kosterlitz-Thouless-type continuous phase transition observed in the three-spin interaction model is discussed. The relevant field theory describes the topological defects involved and enables us to perform the renormalization-group analysis. Based on it, we shall propose the finite-size-scaling ansatz for the helicity modulus which exhibits the exponent $\barν=3/5$ for the correlation length in the disordered phase. We perform the Monte Carlo simulations to confirm the ansatz. Also, we argue its relevance to the ground-state phase transition in the quantum spin chain.

cond-mat.stat-mech↗

arXiv2007

Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model

We discuss an effective field theory of a triangular-lattice three-spin interaction model defined by the ${\mathbb Z}_p$ variables. Based on the symmetry properties and the ideal-state graph concept, we show that the vector dual sine-Gordon model describes the long-distance properties for $p\ge5$; we then compare its predictions with the previous argument. To provide the evidences, we numerically analyze the eigenvalue structure of the transfer matrix for $p=6$, and we check the criticality with the central charge $c=2$ of the intermediate phase and the quantization condition of the vector charges.

cond-mat.stat-mech↗

arXiv2006

Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

cond-mat.stat-mech↗

arXiv2006

Monte Carlo study of the antiferromagnetic three-state Potts model with staggered polarization field on the square lattice

Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF) three-state Potts model with a staggered polarization field on the square lattice. We obtain two phase transitions; one belongs to the ferromagnetic three-state Potts universality class, and the other to the Ising universality class. The phase diagram obtained is quantitatively consistent with the transfer matrix calculation. The Ising transition in the large nearest-neighbor interaction limit has been made clear by the detailed analysis of the energy density of states.

cond-mat.stat-mech↗

arXiv2006

Field-induced Berezinskii-Kosterlitz-Thouless transition and string-density plateau in the anisotropic triangular antiferromagnetic Ising model

The field-induced Berezinskii-Kosterlitz-Thouless (BKT) transition in the ground state of the triangular antiferromagnetic Ising model is studied by the level-spectroscopy method. We analyze dimensions of operators around the BKT line, and estimate the BKT point $H_{\rm c}\simeq0.5229\pm0.001$, which is followed by a level-consistency check to demonstrate the accuracy of our estimate. Further we investigate the anisotropic case to clarify the stability of the field-induced string-density plateau against an incommensurate liquid state by the density-matrix renormalization-group method.

cond-mat.stat-mech↗