arXiv subjects

Yusuke Tomita

Publications and source records attributed to Yusuke Tomita.

At least 19 recordsLinked to original sources

arXiv2025

Ferroaxial order of the monolayer ice in martyite

Ice Ih, the most stable phase of water at ambient pressure, is a stacking of the honeycomb network of water molecules H2O. What if one layer of ice is exfoliated and confined to a two-dimensional (2D) sheet? Martyite Zn3(V2O7)(OH)2 2H2O, a mineral with the honeycomb lattice of H2O in the porous framework, is an ideal system for studying such monolayer ice. Due to the geometrical frustration and 2D nature, H2O molecules are dynamically disordered at room temperature. In this study, we reveal disorder-order transitions of H2O in martyite using single-crystal x-ray diffraction (XRD). The XRD results visualize the formation of hydrogen-bonded toroidal H2O hexamers, leading to the ferroaxial order below 200 K. Combined with the molecular dynamics simulations, we discuss the formation process of the H2O hexamers and how they compromise the molecular arrangement towards lower temperatures. Our results unveil the ground state of monolayer ice, a fundamental knowledge to understand the polymorphism of H2O.

cond-mat.mtrl-sci↗

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

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

Temperature scaling in nonequilibrium relaxation in three-dimensional Heisenberg model in the Swendsen-Wang and Metropolis algorithms

Recently, the present authors proposed the nonequilibrium-to-equilibrium scaling (NE-ES) scheme for critical Monte Carlo relaxation process, which scales relaxation data in the whole simulation-time regions regardless of functional forms, namely both for the stretched-exponential critical relaxation in cluster algorithms and for the power-law critical relaxation in local-update algorithms. In the present study, we generalize this scheme to off-critical relaxation process, and scale relaxation data for various temperatures in the whole simulation-time regions. This is the first proposal of the off-critical scaling in cluster algorithms, which cannot be described by the dynamical finite-size scaling theory based on the power-law critical relaxation. As an example, we investigate the three-dimensional Heisenberg model previously analyzed with the NE-ES [Y. Nonomura and Y. Tomita, Phys. Rev. E 93, 012101 (2016)] in the Swendsen-Wang and Metropolis algorithms.

cond-mat.stat-mech↗

arXiv2019

Nonequilibrium-relaxation approach to quantum phase transitions: Nontrivial critical relaxation in cluster-update quantum Monte Carlo

Although the nonequilibrium relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that relaxation process based on cluster-update quantum Monte Carlo (QMC) algorithms, which are now standards in Monte Carlo studies on quantum systems, has been considered "too fast" for such analyses. Recently the present authors revealed that the NER process in classical spin systems based on cluster-update algorithms is characterized by the stretched-exponential critical relaxation, rather than the conventional power-law one in local-update algorithms. In the present article we show that this is also the case in quantum phase transitions analyzed with the cluster-update QMC, and that advantages of NER analyses are available. As the simplest example of isotropic quantum spin models which exhibit quantum phase transitions, we investigate the Néel-dimer quantum phase transition in the two-dimensional $S=1/2$ columnar-dimerized antiferromagnetic Heisenberg model with the continuous-time loop algorithm.

cond-mat.stat-mech↗

arXiv2018

Critical Nonequilibrium Cluster-flip Relaxations in Ising Models

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched-exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

cond-mat.stat-mech↗

arXiv2018

Cluster nonequilibrium relaxation in Ising models observed with the Binder ratio

The Binder ratios exhibit discrepancy from the Gaussian behavior of the magnetic cumulants, and their size independence at the critical point has been widely utilized in numerical studies of critical phenomena. In the present article we reformulate the nonequilibrium relaxation (NER) analysis in cluster algorithms using the $(2,1)$-Binder ratio, and apply this scheme to the two- and three-dimensional Ising models. Although the stretched-exponential relaxation behavior at the critical point is not explicitly observed in this quantity, we find that there exists a logarithmic finite-size scaling formula which can be related with a similar formula recently derived in cluster NER of the correlation length, and that the formula enables precise evaluation of the critical point and the stretched-exponential relaxation exponent $σ$. Physical background of this novel behavior is explained by the simulation-time dependence of the distribution function of magnetization in two dimensions and temperature dependence of $σ$ obtained from magnetization in three dimensions.

cond-mat.stat-mech↗

arXiv2018

Measurement of entanglement entropy in the two-dimensional Potts model using wavelet analysis

We introduce a method to measure the entanglement entropy using a wavelet analysis. In the method we perform the two-dimensional Haar wavelet transform of configuration of Fortuin-Kasteleyn (FK) clusters. The configuration represents a direct snapshot of spin-spin correlations since spin degrees of freedom are traced out in FK representation. A snapshot of FK clusters loses image information at each coarse-graining process by the wavelet transform. We show that the loss of image information measures the entanglement entropy in the Potts model.

cond-mat.stat-mech↗

arXiv2017

Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers

We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling $J_{\rm A}$ and the ferromagnetic (FM) one $J_{\rm B}$ for the respective layers, which are coupled by the interlayer interaction $J_{\rm AB}$ by using Monte Carlo simulations. When $J_{\rm A}$ and $J_{\rm B}$ are of the same order, the unfrustrated FM plane orders first at a high temperature $T_{c1} \sim J_{\rm B}$. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below $T_{c2}$. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-like pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in $\propto \JA / T$ is controlled by a line of Gaussian fixed points at $T = 0$. In the crossover region, a continuous variation in the effective critical exponent $4/9 \lesssim η^{\rm eff} \lesssim 1/2$ is observed. The phase diagram by changing the ratio $J_{\rm A}/J_{\rm B}$ is also investigated.

cond-mat.stat-mech↗

arXiv2016

Relaxational processes in the one-dimensional Ising model with long-range interactions

Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter $σ$, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of $σ$. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.

cond-mat.stat-mech↗

arXiv2015

Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D $q=5$ Potts model, and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the 3D and 4D XY models and in the 2D $q$-state Potts models for $2 \le q \le 4$, and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D $q=5$ and $6$ Potts models, and propose a quantitative criterion on "weakness" of the first-order phase transition.

cond-mat.stat-mech↗

arXiv2015

Nonequilibrium behaviors of 3D Heisenberg model in the Swendsen-Wang algorithm

Recently Y. N. showed that the nonequilibrium critical relaxation of the 2D Ising model from the perfectly-ordered state in the Wolff algorithm is described by the stretched-exponential decay, and found a universal scaling scheme to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. In order to evaluate the critical temperature and critical exponents precisely with the above scaling scheme, we calculate the nonequilibrium ordering from the perfectly-disordered state in the Swendsen-Wamg algorithm, and find that the critical ordering process is described by the stretched-exponential growth with the comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies.

cond-mat.stat-mech↗

arXiv2014

Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder

Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disorder, which is analyzed by classical Monte Carlo simulations. First, we discuss the phase diagrams as well as thermodynamic and magnetic properties. We show that the spin-glass transition temperature is largely enhanced by the spin-lattice coupling $b$ in the weakly disordered regime. This enhancement is ascribed to the suppression of thermal fluctuations in semidiscrete degenerate manifold formed in the presence of the spin-lattice coupling. We also find that, as increasing the strength of disorder, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by $b$, being almost independent of bond disorder. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in the spin-lattice order in the weakly disordered regime, the concomitant transition remains robust. We investigate the nature of the concomitant transition by analyzing the hysteresis of the magnetic susceptibility, the nonlinear susceptibility, and the specific heat. Furthermore, we discuss linear and nonlinear magnetic susceptibilities in the high-temperature paramagnetic phase as well as single-spin flip dynamics in the nematic phase. All these results are discussed in comparison with experiments for typical pyrochlore magnets, such as Y2Mo2O7 and ZnCr2O4.

cond-mat.str-el↗

arXiv2014

Incommensurate Short-Range Order in $S=1$ Triangular Lattice Ising Antiferromagnet

We study the $S = 1$ triangular lattice Ising antiferromagnet by Monte Carlo simulations. Frustrations between a major antiferromagnetic third-neighbor interaction $J_3$ and a minor ferromagnetic nearest-neighbor interaction $J_1$ cause incommensurate short-range orders at intermediate temperatures. At low temperatures (below $T/J_3 \lesssim 0.2$ for $J_1/J_3 = -1/3$), the system exhibits fourfold periodic ordered state. In the short-range order phase, the system shows a glassy two-step relaxation. We demonstrate that the features of the short-range order are attributed to the cooperation between the frustrations and the nonmagnetic Ising spin states which is a particular feature of the integer spin systems.

cond-mat.stat-mech↗

arXiv2013

Response to a twist on systems with Zp symmetry

We study response to a twist in the two-dimensional p-state clock model, which has the discrete Zp symmetry. The response is measured in terms of helicity modulus, which is usually defined with respect to an infinitesimal twist. However, we demonstrate that such a definition is inappropriate for the clock model. The helicity modulus must be defined with respect to a finite, quantized twist which matches the discrete Zp symmetry of the model. Recent numerical results, which casted doubt on the standard picture that two Berezinskii-Kosterlitz-Thouless transitions occur for p > 4, are rather a consequence of use of the inappropriate quantity. Numerical calculation of the appropriately defined helicity modulus indeed supports the standard picture.

cond-mat.stat-mech↗

arXiv2013

Relaxor behavior and morphotropic phase boundary in a simple model

A simple model to reproduce strong enhancement of dielectric response near the morphotropic phase boundary (MPB) is proposed. This model consists of long-range dipole-dipole interaction and compositional chemical disorder incorporated by the variation in lengths of dipole moments. By applying Monte Carlo simulation, we show that there appears a ferroelectric boundary phase between two types of antiferroelectric phases at an optimal strength of randomness. In the boundary phase, ferroelectric domain becomes remarkably large and flexible to external electric fields, leading to huge dielectric response. This observation indicates that huge dielectric response near the MPB originates from {\it local} polarization rotation under suppressed anisotropy by phase competition.

cond-mat.mtrl-sci↗

arXiv2012

Weak Spin Fluctuation with Finite Wave Vector and Superconducting Gap Symmetry in KxFe2-ySe2: 77Se Nuclear Magnetic Resonance

We report $^{77}$Se-nuclear magnetic resonance (NMR) results down to sufficiently low temperatures under magnetic fields parallel to both the $ab$-plane and the c-axis in a paramagnetic/superconducting (PM/SC) phase of K$_x$Fe$_{2-y}$Se$_2$. The observation of anisotropy in the orbital part of the Knight shift results in the anisotropy of its spin part increasing on approaching the transition temperature. The anisotropy of the Korringa relation suggests the presence of the weak spin fluctuations with a finite wave vector $\bm{q}$, which induce the magnetic fluctuations along the ab-plane at the Se site. Such fluctuations do not correspond to the stripe $(π,0)$ correlation of the Fe moment observed in many Fe-based superconductors, and are not contradictory to weak $(π,π)$ correlations. The nuclear spin-lattice relaxation rate $1/T_1$ shows a field-independent $T_1T \sim const.$ behavior at low temperatures for $H \parallel ab$, which is attributed to the nonzero density of states at the Fermi level and can be explained by the sign-changing order parameter even for nodeless gaps. The temperature dependence of $1/T_1$ is reproduced well by nodeless models with two isotropic gaps or a single anisotropic gap. The obtained gap magnitude in the isotropic two-gap model is comparable to those obtained in the angle-resolved photoemission spectroscopy experiments.

cond-mat.supr-con↗