arXiv subjects

Yoshihiko Nishikawa

Publications and source records attributed to Yoshihiko Nishikawa.

15 recordsLinked to original sources

arXiv2026

Dynamical Criticality of a Machine-learning-assisted Monte Carlo algorithm for a Mean-Field Spin Glass model

We critically assess the performance of an autoregressive generative neural network model by applying it to an antiferromagnetic Ising model on a random regular graph. We train the network on equilibrium configurations in the low-temperature spin-glass phase of the model and perform Monte Carlo simulations using spin configurations generated by the network. The relaxation time of the Monte Carlo simulations drastically decreases with increasing the size of the training dataset and converges to an optimal value. The dynamical exponent characterizing the growth of the optimal relaxation time as a function of the system size is slightly reduced compared to the local Monte Carlo dynamics. However, we find that the size of the training dataset to achieve the optimal performance grows much faster with the system size than the relaxation time, implying that the total training cost eventually hinders a practical use of the method at large system sizes.

cond-mat.dis-nn↗

arXiv2026

Phase transition in large language models and the criticality of natural languages

Generation of text and speech in natural languages can be modeled as a stochastic process. This idea dates back to the seminal work of Markov and, later, to that of Shannon and also underlies the recent development of large language models (LLMs). The stochastic processes corresponding to natural languages should be distinct from those that generate nonlinguistic sequences. One of the features that discriminate linguistic and nonlinguistic sequences is power-law behavior, which is universally observed across different languages. In statistical physics, such behavior suggests that natural languages are critical: They lie near a phase transition point in a parametrized space of stochastic processes. However, testing this conjecture is not straightforward. A phase transition, even if it exists, cannot be directly observed in real-world natural languages because they do not have any controllable parameters. Here, we use LLMs as controllable effective models of natural languages. Through statistical analyses of texts generated by LLMs, we find that, when a parameter analogous to physical temperature is varied, LLMs undergo a phase transition. The transition separates a low-temperature phase with complex repetitive structures in generated texts from a high-temperature phase in which LLMs generate incomprehensible texts. At the critical point between these phases, generated texts display the power-law behavior similar to that of natural languages and most closely resemble natural languages as measured by a standard metric in natural language processing. These findings strongly suggest that natural languages are indeed critical.

cond-mat.dis-nn↗

arXiv2025

Irreversible swap algorithms for soft sphere glasses

We extend to soft repulsive interaction potentials a recently proposed irreversible swap algorithm originally designed for polydisperse hard spheres. The original algorithm performs rejection-free, irreversible, collective swap moves. We show that event-driven cluster updates of particle diameters can also be performed in continuous potentials by introducing a factorised Metropolis probability. However, the Metropolis factorisation needed to deal with continuous potentials decreases the efficiency of the algorithm and mitigates the benefits of breaking detailed balance. This leads us to propose another irreversible swap algorithm using the standard Metropolis probability that accelerates the relaxation of soft sphere glasses at low temperatures, compared to the original swap algorithm. We apply these efficient swap algorithms to produce very stable inherent structures with vibrational density of states lacking the quasi-localised excitations observed in conventional glasses.

cond-mat.soft↗

arXiv2024

Collective relaxation dynamics in a three-dimensional lattice glass model

We numerically elucidate the microscopic mechanisms controlling the relaxation dynamics of a three-dimensional lattice glass model that has static properties compatible with the approach to a random first-order transition. At low temperatures, the relaxation is triggered by a small population of particles with low-energy barriers forming mobile clusters. These emerging quasiparticles act as facilitating defects responsible for the spatially heterogeneous dynamics of the system, whose characteristic lengthscales remain strongly coupled to thermodynamic fluctuations. We compare our findings both with existing theoretical models and atomistic simulations of glass-formers.

cond-mat.dis-nn↗

arXiv2023

Random Postprocessing for Combinatorial Bayesian Optimization

Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the global optimum. Here, we numerically study the effect of a postprocessing method on Bayesian optimization that strictly prohibits duplicated samples in the dataset. We find the postprocessing method significantly reduces the number of sequential steps to find the global optimum, especially when the acquisition function is of maximum a posterior estimation. Our results provide a simple but general strategy to solve the slow convergence of Bayesian optimization for high-dimensional problems.

cs.LG↗

arXiv2023

The Liquid--Hexatic Transition for Soft Disks

We study the liquid--hexatic transition of soft disks with massively parallel simulations and determine the equation of state as a function of system size. For systems with interactions decaying as the inverse $m$th power of the separation, the liquid--hexatic phase transition is continuous for $m = 12$ and $m=8$, while it is of first order for $m = 24$. The critical power $m$ for the transition between continuous and first-order behavior is larger than previously reported. The continuous transition for $ m=12 $ implies that the two-dimensional Lennard-Jones model has a continuous liquid--hexatic transition at high temperatures. We also study the Weeks--Chandler--Andersen model and find a continuous transition at high temperatures, that is consistent with the soft-disk case for $m=12$. Pressure data as well as our implementation are available from an open-source repository.

cond-mat.soft↗

arXiv2022

Hard-disk computer simulations -- a historic perspective

We discuss historic pressure computations for the hard-disk model performed since 1953, and compare them to results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental effort to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository.

cond-mat.stat-mech↗

arXiv2022

Collective dynamics in a glass-former with Mari-Kurchan interactions

We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both non-trivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time-correlation functions display a phenomenology typical of supercooled liquids, including the emergence of an excess signal in relaxation spectra at intermediate frequencies. We show that this evolution is accompanied by strong signatures of collective and heterogeneous dynamics which cannot be interpreted in terms of single particle hopping and emerge from dynamic facilitation. Our study demonstrates that an off-lattice interacting particle model with extremely simple structural correlations displays quantitatively realistic glassy dynamics.

cond-mat.dis-nn↗

arXiv2022

Relaxation dynamics in the energy landscape of glass-forming liquids

We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmonic value at low temperatures. We demonstrate that this apparent evolution is controlled by a temperature-dependent population of localised glassy excitations. Our work unifies several recent lines of studies aiming at a detailed characterisation of the complex potential energy landscape of glass-formers, and challenges both mean-field and real space descriptions of glasses.

cond-mat.stat-mech↗

arXiv2021

Stationary Bootstrap: A Refined Error Estimation for Equilibrium Time Series

In Markov-chain Monte Carlo simulations, estimating statistical errors or confidence intervals of numerically obtained values is an essential task. In this paper, we review several methods for error estimation, such as simple empirical estimation with multiple independent runs, the blocking method, and the stationary bootstrap method. We then study their performance when applied to an actual Monte-Carlo time series. We find that the stationary bootstrap method gives a reasonable and stable estimation for any quantity using only one single time series. In contrast, the simple estimation with few independent runs can be demonstratively erroneous. We further discuss the potential use of the stationary bootstrap method in numerical simulations.

cond-mat.stat-mech↗

arXiv2021

Relaxation dynamics of non-Brownian spheres below jamming

We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless spheres below jamming in spatial dimensions $d=2$, $3$, $4$, and $8$, and in the mean-field Mari-Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite $d$ logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all $d$ in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.

cond-mat.soft↗

arXiv2020

Lattice glass model in three spatial dimensions

The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical dynamics observed in fragile supercooled liquids such as two-step relaxation, super-Arrhenius growth in the relaxation time, and dynamical heterogeneity. Using advanced Monte Carlo methods, we compute the thermodynamic properties deep inside the glassy temperature regime, well below the onset temperature of the slow dynamics. The specific heat has a finite jump towards the thermodynamic limit with critical exponents close to those expected from the hyperscaling and the random first-order transition theory for the glass transition. We also study an effective free energy of glasses, the Franz--Parisi potential, as a function of the overlap between equilibrium and quenched configurations. The effective free energy indicates the existence of a first-order phase transition, consistent with the random first-order transition theory. These findings strongly suggest that the glassy dynamics of the model has its origin in thermodynamics.

cond-mat.stat-mech↗

arXiv2017

Solid--liquid transition of skyrmions in a two-dimensional chiral magnet

We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional order. However, we show using large-scale Monte Carlo simulations that at small finite temperature, the skyrmions rather form a typical two-dimensional solid: Positional correlations decay with distance as power laws while the orientational correlations remain finite. At higher temperature, we observe a direct transition from this two-dimensional solid to a liquid with short-range correlations. This differs from generic two-dimensional homogeneous particle systems, where a hexatic phase is realized between the solid and the liquid.

cond-mat.stat-mech↗

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↗

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↗