arXiv subjects

Yutaka Okabe

Publications and source records attributed to Yutaka Okabe.

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

Comment on CFT in AdS and boundary RG flows: O(1/N) Result

In a recent paper [JHEP 11 (2020) 118], S. Giombi and H. Khanchandani studied the 1/N expansion of the O(N) model in semi-infinite space within the framework of conformal field theory in anti-de Sitter space. They presented a series expansion for the O(1/N) correction to the boundary anomalous dimension in the case of the ordinary transition. Although they were unable to sum the series or simplify its form analytically, they demonstrated numerically that their result matches our earlier, simple analytic expression given in Prog. Theor. Phys. 70 (1983) 1226. In this paper, we show that their series expansion is in fact exactly equivalent to our original expression. However, since the final formula in eq. (4.57) of their paper, which is expressed in terms of two different 3F2 functions, cannot produce the correct values, we derive the correct formulae involving two 3F2 functions in the Appendices. We comment on the similarity and difference between their analysis and ours in the cases of the ordinary and special transitions, and present full details of deriving the anomalous dimension for all the cases including the extraordinary transition, which were not written in our earlier paper.

hep-th↗

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↗

arXiv2024

Ising model on the aperiodic Smith hat

Smith et al discovered an aperiodic monotile of 13-sided shape in 2023. It is called the `Smith hat' and consists of 8 kites. We deal with the statistical physics of the lattice of the kites, which we call the `Smith-kite lattice'. We studied the Ising model on the aperiodic Smith-kite lattice and the dual Smith-kite lattice using Monte Carlo simulations. We combined the Swendsen-Wang multi-cluster algorithm and the replica exchange method. We simulated systems up to the total spin number $939201$. Using the finite-size scaling analysis, we estimated the critical temperature on the Smith-kite lattice as $T_c/J=2.405 \pm 0.0005$ and that of the dual Smith-kite lattice as $T^{*}_{c}/J=2.143 \pm 0.0005$. Moreover, we confirmed the duality relation between the critical temperatures on the dual pair of aperiodic lattices, $\sinh(2J/T_c) \sinh(2J/T^{*}_{c}) = 1.000 \pm 0.001$. We also checked the duality relation for the nearest-neighbor correlation at the critical temperature, essentially the energy, $\epsilon(T_c)/\coth(2J/T_c) + \epsilon(T^{*}_c)/\coth(2J/T^{*}_c) = 1.000 \pm 0.001$.

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↗

arXiv2021

Spread of variants of epidemic disease based on the microscopic numerical simulations on networks

Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of variants. Assume that a small number of individuals infected with the variant are added to widespread infection with the original virus. When a highly infectious variant that is more transmissible than the original lineage is added, the variant spreads quickly to the wide space. On the other hand, if the infectivity is about the same as that of the original virus, the infection will not spread. The rate of spread is not linear as a function of the infection strength but increases non-linearly. This cannot be explained by the compartmental model of epidemiology but can be understood in terms of the dynamic absorbing state known from the contact process.

q-bio.PE↗

arXiv2021

Super-resolution of spin configurations based on flow-based generative models

We present a super-resolution method for spin systems using a flow-based generative model that is a deep generative model with reversible neural network architecture. Starting from spin configurations on a two-dimensional square lattice, our model generates spin configurations of a larger lattice. As a flow-based generative model precisely estimates the distribution of the generated configurations, it can be combined with Monte Carlo simulation to generate large lattice configurations according to the Boltzmann distribution. Hence, the long-range correlation on a large configuration is reduced into the shorter one through the flow-based generative model. This alleviates the critical slowing down near the critical temperature. We demonstrated 8 times increased lattice size in the linear dimensions using our super-resolution scheme repeatedly. We numerically show that by performing simulations for $16\times 16$ configurations, our model can sample lattice configurations at $128\times 128$ on which the thermal average of physical quantities has good agreement with the one evaluated by the traditional Metropolis-Hasting Monte Carlo simulation.

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

Weakly-supervised learning on Schrodinger equation

We propose a machine learning method to solve Schrodinger equations for a Hamiltonian that consists of an unperturbed Hamiltonian and a perturbation. We focus on the cases where the unperturbed Hamiltonian can be solved analytically or solved numerically with some fast way. Given a potential function as input, our deep learning model predicts wave functions and energies using a weakly-supervised method. Information of first-order perturbation calculation for randomly chosen perturbations is used to train the model. In other words, no label (or exact solution) is necessary for the training, which is why the method is called weakly-supervised, not supervised. The trained model can be applied to calculation of wave functions and energies of Hamiltonian containing arbitrary perturbation. As an example, we calculated wave functions and energies of a harmonic oscillator with a perturbation and results were in good agreement with those obtained from exact diagonalization.

cond-mat.stat-mech↗

arXiv2021

Inverse Renormalization Group based on Image Super-Resolution using Deep Convolutional Networks

The inverse renormalization group is studied based on the image super-resolution using the deep convolutional neural networks. We consider the improved correlation configuration instead of spin configuration for the spin models, such as the two-dimensional Ising and three-state Potts models. We propose a block-cluster transformation as an alternative to the block-spin transformation in dealing with the improved estimators. In the framework of the dual Monte Carlo algorithm, the block-cluster transformation is regarded as a transformation in the graph degrees of freedom, whereas the block-spin transformation is that in the spin degrees of freedom. We demonstrate that the renormalized improved correlation configuration successfully reproduces the original configuration at all the temperatures by the super-resolution scheme. Using the rule of enlargement, we repeatedly make inverse renormalization procedure to generate larger correlation configurations. To connect thermodynamics, an approximate temperature rescaling is discussed. The enlarged systems generated using the super-resolution satisfy the finite-size scaling.

cond-mat.stat-mech↗

arXiv2020

Machine-Learning Study using Improved Correlation Configuration and Application to Quantum Monte Carlo Simulation

We use the Fortuin-Kasteleyn representation based improved estimator of the correlation configuration as an alternative to the ordinary correlation configuration in the machine-learning study of the phase classification of spin models. The phases of classical spin models are classified using the improved estimators, and the method is also applied to the quantum Monte Carlo simulation using the loop algorithm. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition of the spin 1/2 quantum XY model on the square lattice. We classify the BKT phase and the paramagnetic phase of the quantum XY model using the machine-learning approach. We show that the classification of the quantum XY model can be performed by using the training data of the classical XY model.

cond-mat.stat-mech↗

arXiv2020

Two-size Probability-Changing Cluster Algorithm

We propose a self-adapted Monte Carlo approach to automatically determine the critical temperature by simulating two systems with different sizes at the same temperature. The temperature is increased or decreased by checking the short-time average of the correlation ratios of the two system sizes. The critical temperature is achieved using the negative feedback mechanism, and the thermal average near the critical temperature can be calculated precisely. The proposed approach is a general method to treat second-order phase transition, first-order phase transition, and Berezinskii-Kosterlitz-Thouless transition on the equal footing.

cond-mat.stat-mech↗

arXiv2020

Machine-Learning Studies on Spin Models

With the recent developments in machine learning, Carrasquilla and Melko have proposed a paradigm that is complementary to the conventional approach for the study of spin models. As an alternative to investigating the thermal average of macroscopic physical quantities, they have used the spin configurations for the classification of the disordered and ordered phases of a phase transition through machine learning. We extend and generalize this method. We focus on the configuration of the long-range correlation function instead of the spin configuration itself, which enables us to provide the same treatment to multi-component systems and the systems with a vector order parameter. We analyze the Berezinskii-Kosterlitz-Thouless (BKT) transition with the same technique to classify three phases: the disordered, the BKT, and the ordered phases. We also present the classification of a model using the training data of a different model.

cond-mat.stat-mech↗

arXiv2019

Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models

We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for characterizing the existence of Berezinskii-Kosterlitz-Thouless (BKT) phase and its transitions by large-scale Monte Carlo simulations. We discuss the advantage of correlation ratio in comparison to other commonly used quantities in probing BKT transition. Using finite size scaling of BKT type transition, we estimate transition temperatures and corresponding exponents. The comparison between the results from both types revealed that the existing transitions belong to BKT universality.

cond-mat.stat-mech↗

arXiv2018

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the "kagome-ice" problem. We discuss the similarity and dissimilarity of the magnetization curves of the "kagome-ice" state and the two-dimensional kagome lattice.

physics.comp-ph↗

arXiv2017

Study of spin models with polyhedral symmetry on square lattice

Anisotropy is important for the existence of true long range order in two dimensional (2D) systems. This is firmly exemplified by the $q$-state clock models in which discreteness drives the quasi-long range order into a true long range order at low temperature for $q> 4$. Previously we studied 2D edge-cubic spin model, which is one of the discrete counterpart of the continuous Heisenberg model, and observed two finite temperature phase transitions, each corresponds to the breakdown of octahedral ($O_h$) symmetry and $C_{3h}$ symmetry, which finally freezes into ground state configuration. The present study investigates discret models with polyhedral symmetry, obtained by e equally partioning the $4π$ of the solid angle of a sphere. There are five types of models if spins are only allowed to point to the vertices of the polyhedral structures such as Tetrahedron, Octahedron, Hexahedron, Icosahedron and Dodecahedron. By using Monte Carlo simulation with cluster algorithm we calculate order parameters and estimate the critical temperatures exponents of each model. We found a systematic decrease in critical temperatures as the number of spin states increases (from the Tetrahedral to Dodecahedral spin model).

cond-mat.stat-mech↗

arXiv2017

Entropy of the diluted antiferromagnetic Ising models on the frustrated lattices using the Wang-Landau method

We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.

cond-mat.str-el↗

arXiv2017

Interplay of dilution and magnetic field in the nearest-neighbor spin-ice model on the pyrochlore lattice

We study the magnetic field effects on the diluted spin-ice materials using the replica-exchange Monte Carlo simulation. We observe five plateaus in the magnetization curve of the diluted nearest-neighbor spin-ice model on the pyrochlore lattice when a magnetic field is applied in the [111] direction. This is in contrast to the case of the pure model with two plateaus. The origin of five plateaus is investigated from the spin configuration of two corner-sharing tetrahedra in the case of the diluted model.

physics.comp-ph↗