arXiv subjects

Koji Hukushima

Publications and source records attributed to Koji Hukushima.

At least 55 records · Page 3Linked to original sources

arXiv2017

Real-space analysis of scanning tunneling microscopy topography datasets using sparse modeling approach

A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$ regularization and $k$-means clustering, enables separation of the peaks and atomic center positioning with accuracy beyond the resolution of the measurement grid. The validity and efficiency of the proposed method are demonstrated using synthetic data in comparison to the conventional least-square method. An application of the proposed method to experimental data of a metallic oxide thin film clearly indicates the existence of defects and corresponding local lattice deformations.

physics.data-an↗

arXiv2017

Method for Estimating Spin-Spin Interactions from Magnetization Curves

We develop a method to estimate the spin-spin interactions in the Hamiltonian from the observed magnetization curve by machine learning based on Bayesian inference. In our method, plausible spin-spin interactions are determined by maximizing the posterior distribution, which is the conditional probability of the spin-spin interactions in the Hamiltonian for a given magnetization curve with observation noise. The conditional probability is obtained by the Markov-chain Monte Carlo simulations combined with an exchange Monte Carlo method. The efficiency of our method is tested using synthetic magnetization curve data, and the results show that spin-spin interactions are estimated with a high accuracy. In particular, the relevant terms of the spin-spin interactions are successfully selected from the redundant interaction candidates by the $l_1$ regularization in the prior distribution.

cond-mat.stat-mech↗

arXiv2016

A Fidelity Susceptibility Approach to Quantum Annealing of NP-hard problems

The computational complexity conjecture of NP $\nsubseteq$ BQP implies that there should be an exponentially small energy gap for Quantum Annealing (QA) of NP-hard problems. We aim to verify how this computation originated gapless point could be understood based on physics, using the quantum Monte Carlo method. As a result, we found a phase transition detectable only by the divergence of fidelity susceptibility. The exponentially small gapless points of each instance are all located in the phase found in this study, which suggests that this phase transition is the physical cause of the failure of QA for NP-hard problems.

quant-ph↗

arXiv2016

Compressed sensing in scanning tunneling microscopy/spectroscopy for observation of quasi-particle interference

We applied a method of compressed sensing to the observation of quasi-particle interference (QPI) by scanning tunneling microscopy/spectroscopy to improve efficiency and save measurement time. To solve an ill-posed problem owing to the scarcity of data, the compressed sensing utilizes the sparseness of QPI patterns in momentum space. We examined the performance of a sparsity-inducing algorithm called least absolute shrinkage and selection operator (LASSO), and demonstrated that LASSO enables us to recover a double-circle QPI pattern of the Ag(111) surface from a dataset whose size is less than that necessary for the conventional Fourier transformation method. In addition, the smallest number of data required for the recovery is discussed on the basis of cross validation.

cond-mat.mes-hall↗

arXiv2016

Typical Performance of Approximation Algorithms for NP-hard Problems

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks. Here three approximation algorithms are examined; the linear-programming relaxation, the loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using the statistical-mechanical technique while the average-case analysis of the last one is studied by the generating function method. These algorithms have a threshold in the typical performance with increasing the average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases determined by the order of the typical-performance thresholds. We provide some conditions for classifying the graph ensembles and demonstrate explicitly examples for the difference in the threshold.

cond-mat.dis-nn↗

arXiv2016

Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions

Phase transitions in a classical Heisenberg spin model of a chiral helimagnet with the Dzyaloshinskii--Moriya (DM) interaction in three dimensions are numerically studied. By using the event-chain Monte Carlo algorithm recently developed for particle and continuous spin systems, we perform equilibrium Monte Carlo simulations for large systems up to about $10^6$ spins. Without magnetic fields, the system undergoes a continuous phase transition with critical exponents of the three-dimensional \textit{XY} model, and a uniaxial periodic helical structure emerges in the low temperature region. In the presence of a magnetic field perpendicular to the axis of the helical structure, it is found that there exists a critical point on the temperature and magnetic-field phase diagram and that above the critical point the system exhibits a phase transition with strong divergence of the specific heat and the uniform magnetic susceptibility.

cond-mat.stat-mech↗

arXiv2016

Statistical-mechanical Analysis of Linear Programming Relaxation for Combinatorial Optimization Problems

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of $α$-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical-mechanical model with a one-parameter family. Statistical-mechanical analyses reveal for $α=2$ that the LP optimal solution is typically equal to that given by the IP below the critical average degree $c=e$ in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result $c=1$, and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with $α\geq 3$, minimum vertex covers on $α$-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree $c=e/(α-1)$ where the replica symmetry is broken.

cond-mat.dis-nn↗

arXiv2016

Irreversible simulated tempering

An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is constructed based on the framework of the skew detailed balance condition. By applying this method to the ferromagnetic Ising model in two dimensions on a square lattice as a benchmark, the dynamical behavior of the inverse temperature and an autocorrelation function of the magnetization are studied numerically. It is found that the relaxation dynamics of the inverse temperature changes qualitatively from diffusive to ballistic by violating the detailed balance condition. Consequently, the autocorrelation time of magnetization is several times smaller than that for the conventional algorithm satisfying the detailed balance condition.

cond-mat.stat-mech↗

arXiv2015

Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions

An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the efficiency of our proposed method, the relaxation dynamics of the slowest mode and the asymptotic variance are studied analytically in a random walk on one dimension. It is found that the performance in irreversible MCMC methods violating the detailed balance condition is improved by appropriately choosing parameters in the algorithm.

cond-mat.stat-mech↗

arXiv2015

Event-chain algorithm for the Heisenberg model: Evidence for $z \simeq 1$ dynamic scaling

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent $z \approx 1$ at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. This seems to be the first report that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of $z\simeq 2$.

cond-mat.stat-mech↗

arXiv2014

Evidence of one-step replica symmetry breaking in a three-dimensional Potts glass model

We study a 7-state Potts glass model in three dimensions with first, second, and third neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a finite temperature T_c, a discontinuous jump of an order parameter at T_c without latent heat, and a non-trivial structure of the order-parameter distribution below T_c. They are compatible with a one-step replica symmetry breaking.

cond-mat.dis-nn↗

arXiv2014

Numerical Detection of the Ergodicity Breaking in a Lattice Glass Model

We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with the ergodicity breaking at an occupation density. The present method invented for a numerical detection of the ergodicity breaking is applicable to glassy systems in finite dimensions.

cond-mat.dis-nn↗

arXiv2013

Typical behavior of the linear programming method for combinatorial optimization problems: From a statistical-mechanical perspective

Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a lattice-gas model on the Erdös-Rényi random graphs is analyzed by a replica method. It is found that the LP optimal solution is typically equal to that of the IP below the critical average degree c*=e in the thermodynamic limit. The critical threshold for LP=IP is beyond a mathematical result, c=1, and coincides with the replica-symmetry-breaking threshold of the IP.

cond-mat.dis-nn↗

arXiv2013

A List Referring Monte Carlo Method for Lattice Glass Models

We present an effcient Monte-Carlo method for lattice glass models which are characterized by hard constraint conditions. The basic idea of the method is similar to that of the $N$-fold way method. By using a list of sites into which we can insert a particle, we avoid trying a useless transition which is forbidden by the constraint conditions. We applied the present method to a lattice glass model proposed by Biroli and M{é}zard. We first evaluated the efficiency of the method through measurements of the autocorrelation function of particle configurations. As a result, we found that the efficiency is much higher than that of the standard Monte-Carlo method. We also compared the efficiency of the present method with that of the $N$-fold way method in detail. We next examined how the efficiency of extended ensemble methods such as the replica exchange method and the Wang-Landau method is inflnuenced by the choice of the local update method. The results show that the efficiency is considerably improved by the use of efficient local update methods. For example, when the number of sites $N_{\rm site}$ is 1024, the ergodic time $τ_{\rm E}$ of the replica exchange method in the grand-canonical ensemble, which is the average round-trip time of a replica in chemical-potential space, with the present local update method is more than $10^2$ times shorter than that with the standard local update method. This result shows that the efficient local update method is quite important to make extended ensemble methods more effective.

cond-mat.stat-mech↗

arXiv2013

Multicanonical sampling of rare events in random matrices

A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random matrices, and matrices whose components are subject to uniform density. Specifically, the probability that all eigenvalues of a matrix are negative is estimated in these cases down to the values of $\sim 10^{-200}$, a region where naive random sampling is ineffective. The method can be applied to any ensemble of matrices and used for sampling rare events characterized by any statistics.

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

Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm

We study minimum vertex cover problems on random α-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase transition at the critical average degree e/(α-1). Below the critical degree, a replica symmetric ansatz in the statistical-mechanical method holdsand the algorithm estimates a solution of the problem which coincide with that by the replica method. In contrast, above the critical degree, the replica symmetric solution becomes unstable and these methods fail to estimate the exact solution.These results strongly suggest a close relation between the replica symmetry and the performance of approximation algorithm.

cond-mat.dis-nn↗

arXiv2013

Dynamics of the One-Dimensional Ising Model without Detailed Balance Condition

We study an irreversible Markov chain Monte Carlo method based on a skew detailed balance condition for an one-dimensional Ising model. Dynamical behavior of the magnetization density is analyzed in order to understand the properties of this method. As a result, it is found theoretically that the relaxation time of the magnetization density is reduced by using some transition probabilities satisfying the skew detailed balance condition, in comparison to that with the corresponding transition probability with the detailed balance condition, and that one of the transition probabilities changes the dynamical critical exponent even with a local spin update.

cond-mat.stat-mech↗