arXiv subjects

Harukuni Ikeda

Publications and source records attributed to Harukuni Ikeda.

At least 19 recordsLinked to original sources

arXiv2026

Solvable model of noisy coupled oscillators with fully random interactions

We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the stationary response and correlation functions. We show that the finite-temperature spin-glass transition is suppressed for any nonmonodisperse natural-frequency distribution, including continuous, discrete, and asymmetric distributions, because the resulting low-frequency singularity of the correlation function is incompatible with the spherical constraint. At zero temperature, however, a spin-glass phase persists for arbitrary frequency dispersion. This residual zero-temperature glassiness is likely a special feature of the spherical dynamics and would be destroyed by local nonlinearities. The model thus provides a solvable oscillator framework for studying how nonequilibrium perturbations suppress finite-temperature glassy freezing.

cond-mat.dis-nn↗

arXiv2026

High-dimensional theory of the glass transition revisited: hopping and local defects

The replicated liquid theory provides a microscopic mean-field description of the glass transition by combining the density functional theory of liquids with the replica method originally developed for spin glasses. In the conventional replica liquid theory, a glassy state is described by assuming that particles in different replicas undergo vibrational motion around common centers of mass, thereby forming molecules that contain one particle from every replica. Here we revisit this assumption by allowing each molecule to contain only a subset of replicas. This generalized formulation describes particle-level replica mismatches, which may be associated with non-vibrational motions such as particle hopping. We apply the theory to high-dimensional hard and harmonic spheres, where the mean-field description is expected to become exact. For hard spheres, replica mismatches destabilize the glassy metastable state and shift the dynamical transition to a significantly higher packing fraction, while leaving the leading thermodynamic glass transition unchanged. The resulting transition density agrees, at leading order in high dimensions, with the recent rigorous lower bound for random sphere packings obtained by Campos, Jenssen, Michelen, and Sahasrabudhe by using a discretized version of greedy Random Sequential Absorption, suggesting an algorithmic interpretation of the transition: grandcanonical dynamics is more efficient in high dimensional spaces than canonical one. For harmonic spheres at finite temperature, the glassy state contains a finite replica-mismatch fraction even at the thermodynamic ideal-glass transition, thereby shifting the transition point from that predicted by the conventional replica ansatz.

cond-mat.dis-nn↗

arXiv2026

Weakly Nonlinear Dynamics of Unstable Modes in Jammed Amorphous Solids

We investigate the structural evolution in jammed amorphous solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.

cond-mat.stat-mech↗

arXiv2026

Dynamical renormalization group analysis of $O(n)$ model in steady shear flow

We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we identify a new stable Gaussian fixed point. This fixed point reproduces the anisotropic scaling of static and dynamical critical exponents for both non-conserved (Model A) and conserved (Model B) order parameters. Notably, the upper critical dimensions are $d_{\text{up}} = 2$ for the non-conserved order parameter (Model A) and $d_{\text{up}} = 0$ for the conserved order parameter (Model B), implying that the mean-field critical exponents are observed even in both $d=2$ and $3$ dimensions. Furthermore, the scaling exponent of the order parameter is negative for all dimensions $d \geq 2$, indicating that shear flow stabilizes the long-range order associated with continuous symmetry breaking even in $d = 2$. In other words, the lower critical dimensions are $d_{\rm low} < 2$ for both types of order parameters. This contrasts with equilibrium systems, where the Hohenberg -- Mermin -- Wagner theorem prohibits continuous symmetry breaking in $d = 2$.

cond-mat.stat-mech↗

arXiv2025

Charge glass from supercooling topological-ordered liquid

Topological order characterizes a class of quantum and classical many-body liquid states that escape the conventional classification by spontaneous symmetry breaking. Many properties of the topological-ordered states still await a clear understanding, and nature of phase transition dynamics is one of them. Normally, when a liquid freezes into a solid, crystallization starts with nucleation and a solid domain quickly grows on the surface of the expanding nucleus, and the domains evolve into macroscopic size. In this work, we reveal that the crystallization of the topological-ordered liquid proceeds in a fundamentally different way. The topological-ordered phase is characterized by a global conserved quantity and its conjugate fractional charge, which we call a flux and a triplet in our working system of the charge Ising model on a triangular lattice. In contrast to the normal crystallization process, the phase transition is driven by the diffusive motion of triplets, which is required to change the value of conserved fluxes to exit the topological-ordered phase. In order to complete crystallization, triplets must spend a divergently long time to diffuse over a macroscopic distance across the system, which results in glassy behavior. Reflecting the diffusive motion of triplets, the initial crystallization process shows slowing down with unusually small Avrami exponent $\sim0.5$. These anomalous dynamics are specific to the crystallization from topological-ordered liquid, and well account for the main features of charge glass behavior exhibited by the organic conductors, $θ$-(BEDT-TTF)$_2$X(SCN)$_4$.

cond-mat.stat-mech↗

arXiv2025

Delocalization Induced by Enhanced Hyperuniformity in One-Dimensional Disordered Systems

In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic potentials. In tight-binding chains, strong hyperuniformity induces a sharp delocalization transition and the emergence of mobility edges. The transition is identified by the generalized fractal dimension and corroborated by the scaling of localization length and transmittance. Hyperuniform disorder thus provides a general mechanism for engineering mobility edges and controlling transport in low dimensions.

cond-mat.dis-nn↗

arXiv2025

Interaction-free ergodicity-breaking driven by temporally hyperuniform noise

We show that norm-conserving spin models driven by temporally hyperuniform noise exhibit a sharp ergodicity-breaking transition in the absence of interactions. In the nonergodic phase, the dynamics freeze into configurations determined by the initial condition. Our analysis demonstrates that such interaction-free ergodicity breaking arises generically whenever a global constraint is imposed and the driving noise is class-I hyperuniform, the strongest form in Torquato's classification. The transition can also be interpreted as a condensation of fluctuations into the zero-frequency mode, reminiscent of Bose--Einstein condensation in an ideal gas.

cond-mat.stat-mech↗

arXiv2025

Quantum fluctuations can enhance or reduce positional uncertainty at finite temperature

The uncertainty principle guarantees a non-zero value for the positional uncertainty, $\left\langle Δx^2\right\rangle > 0$, even without thermal fluctuations. This implies that quantum fluctuations inherently enhance positional uncertainty at zero temperature. A natural question then arises: what happens at finite temperatures, where the interplay between quantum and thermal fluctuations may give rise to complex and intriguing behaviors? To address this question, we systematically investigate the positional uncertainty, $\left\langleΔx^2\right\rangle$, of a particle in equilibrium confined within a nonlinear potential of the form $V(x) \propto x^n$, where $n = 2, 4, 6, \dots$ represents an even exponent. Using path integral Monte Carlo simulations, we calculate $\left\langleΔx^2\right\rangle$ in equilibrium as a function of the thermal de Broglie wavelength $Λ$. Interestingly, for large values of $n$, $\left\langleΔx^2\right\rangle$ exhibits a non-monotonic dependence on $Λ$: it initially decreases with increasing $Λ$ at small $Λ$ but increases at larger $Λ$. To further understand this behavior, we employ a semiclassical approximation, which reveals that quantum fluctuations can reduce positional uncertainty for small $Λ$ when the nonlinearity of the potential is sufficiently strong. Finally, we discuss the potential implications of this result for many-body phenomena driven by strong nonlinear interactions, such as glass transitions, where the transition densities exhibit a similar non-monotonic dependence on $Λ$.

cond-mat.stat-mech↗

arXiv2024

Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model

We investigate the scaling behavior of Nambu-Goldstone (NG) modes in the ordered phase of the Vicsek model, introducing a phenomenological equation of motion (EOM) incorporating a previously overlooked non-linear term. This term arises from the interaction between velocity fields and density fluctuations, leading to new scaling behaviors. We derive exact scaling exponents in two dimensions, which reproduce the isotropic scaling behavior reported in a prior numerical simulation.

cond-mat.soft↗

arXiv2024

Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces

The driving forces of chiral active particles and deformations of cells are often modeled by spatially inhomogeneous but temporally periodic driving forces. Such inhomogeneous oscillatory driving forces have only recently been proposed in the context of active matter, and their effects on the systems are not yet fully understood. In this work, we theoretically study the impact of spatially inhomogeneous oscillatory driving forces on continuous symmetry breaking. We first analyze the linear model for the soft modes in the ordered phase to derive the lower critical dimension of the model, and then analyze the spherical model to investigate more detailed phase behaviors. Interestingly, our analysis reveals that symmetry breaking occurs even in one and two dimensions, where the Hohenberg--Mermin--Wagner theorem prohibits continuous symmetry breaking in equilibrium. Furthermore, fluctuations of conserved quantities, such as density, are anomalously suppressed in the long-wavelength, {\it i.e.}, show hyperuniformity.

cond-mat.stat-mech↗

arXiv2024

Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity

In one dimension, particles can not bypass each other. As a consequence, the mean-squared displacement (MSD) in equilibrium shows sub-diffusion ${\rm MSD}(t)\sim t^{1/2}$, instead of normal diffusion ${\rm MSD}(t)\sim t$. This phenomenon is the so-called single-file diffusion. Here, we investigate how the above equilibrium behaviors are modified far from equilibrium. In particular, we want to uncover what kind of non-equilibrium driving force can suppress diffusion and achieve the long-range crystalline order in one dimension, which is prohibited by the Mermin-Wagner theorem in equilibrium. For that purpose, we investigate the harmonic chain driven by the following four types of driving forces that do not satisfy the detailed balance: (i) temporally correlated noise with the noise spectrum $D(ω)\sim ω^{-2θ}$, (ii) conserving noise, (iii) periodic driving force, and (iv) periodic deformations of particles. For the driving force (i) with $θ>-1/4$, we observe ${\rm MSD}(t)\sim t^{1/2+2θ}$ for large $t$. On the other hand, for the driving forces (i) with $θ<-1/4$ and (ii)-(iv), MSD remains finite. As a consequence, the harmonic chain exhibits the crystalline order even in one dimension. Furthermore, the density fluctuations of the model are highly suppressed in a large scale in the crystal phase. This phenomenon is known as hyperuniformity. We discuss that hyperuniformity of the noise fluctuations themselves is the relevant mechanism to stabilize the long-range crystalline order in one dimension and yield hyperuniformity of the density fluctuations.

cond-mat.stat-mech↗

arXiv2024

Comment on "A new universality class describes Vicsek's flocking phase in physical dimensions''

In a recent preprint, ``A new universality class describes Vicsek's flocking phase in physical dimensions'', Patrick Jentsch and Chiu Fan Lee have computed the critical exponents of the Vicsek model in the ordered phase by means of functional renormalization group methods. In this note, we compare their results with our previous theoretical predictions for the Vicsek model, which is expected to be exact in $d=2$ dimensions. We point out that the critical exponents predicted by the two theories are extremely close in both $d=2$ and $3$ dimensions. We found that both theories fit the current numerical data equally well. Extensive numerical simulations for larger system sizes are thus highly desirable to judge which theory is correct.

cond-mat.soft↗

arXiv2024

Scaling theory of continuous symmetry breaking under advection

In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling arguments. For an example of the liner advection, we consider the $O(n)$ model in the steady shear. Our scaling analysis reveals that the model can undergo the continuous symmetry breaking even in $d=2$ and, moreover, predicts the upper critical dimension $d_{\rm up}=2$. These results are fully consistent with a recent numerical simulation of the $O(2)$ model, where the mean-field critical exponents are observed even in $d=2$. For an example of the non-linear advection, we consider the Toner-Tu hydrodynamic theory, which was introduced to explain polar-ordered flocks, such as the Vicsek model. Our simple scaling argument reproduces the previous results by the dynamical renormalization theory. Furthermore, we discuss the effects of the additional non-linear terms discovered by the recent re-analysis of the hydrodynamic equation. Our scaling argument predicts that the additional non-linear terms modify the scaling exponents and, in particular, recover the isotropic scaling reported in a previous numerical simulation of the Vicsek model. We discuss that the critical exponents predicted by the naive scaling theory become exact in $d=2$ by using a symmetry consideration and similar argument proposed by Toner and Tu.

cond-mat.stat-mech↗

arXiv2023

Correlated Noise and Critical Dimensions

In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetry breaking for all dimensions $d\leq 2$. In this work, we discuss that this limitation can be circumvented in non-equilibrium systems driven by the spatio-temporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the $O(n)$ model driven by the spatio-temporally correlated noise by means of the dimensional analysis. Next, we consider the spherical model, which corresponds to the large $n$ limit of the $O(n)$ model and allows us to compute the critical dimensions and critical exponents, analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time, and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.

cond-mat.stat-mech↗

arXiv2023

Control parameter dependence of fluctuation near jamming

The fluctuations of the physical quantities play a central role to characterize the critical phenomena. Here, we report that the nature of the fluctuation highly depends on the control parameter near the jamming transition point $φ_J$. We show that the fluctuations do not diverge when the pressure is used as the control parameter. On the contrary, if the distance to the transition point $φ_J$ is used as the control parameter, the fluctuations show the power-law divergence.

cond-mat.soft↗

arXiv2023

Bose-Einstein-Like condensation of deformed random matrix: A replica approach

In this work, we investigate a symmetric deformed random matrix, which is obtained by perturbing the diagonal elements of the Wigner matrix. The eigenvector $\mathbf{x}_{\rm min}$ of the minimal eigenvalue $λ_{\rm min}$ of the deformed random matrix tends to condensate at a single site. In certain types of perturbations and in the limit of the large components, this condensation becomes a sharp phase transition, the mechanism of which can be identified with the Bose-Einstein condensation in a mathematical level. We study this Bose-Einstein like condensation phenomenon by means of the replica method. We first derive a formula to calculate the minimal eigenvalue and the statistical properties of $\mathbf{x}_{\rm min}$. Then, we apply the formula for two solvable cases: when the distribution of the perturbation has the double peak, and when it has a continuous distribution. For the double peak, we find that at the transition point, the participation ratio changes discontinuously from a finite value to zero. On the contrary, in the case of a continuous distribution, the participation ratio goes to zero either continuously or discontinuously, depending on the distribution.

cond-mat.dis-nn↗

arXiv2022

Active Spherical Model

The spherical model is a popular solvable model and has been applied to describe several critical phenomena such as the ferromagnetic transition, Bose-Einstein condensation, spin-glass transition, glass transition, jamming transition, and so on. Motivated by recent developments of active matter, here we consider the spherical model driven by the Ornstein-Uhlenbeck type self-propulsion force with persistent time $τ_p$. We show that the model exhibits the Ising universality for finite $τ_p$. On the contrary, the model exhibits the random field Ising universality in the limit $τ_p\to\infty$.

cond-mat.stat-mech↗

arXiv2022

Universality of classical and quantum SAT-UNSAT transitions of convex continuous satisfaction problems

Here we investigate the single-layer linearized perceptron near the SAT-UNSAT transition point as a prototypical model of the convex continuous satisfaction problems. The simplicity of the model allows us to take into account the effects of the quantum fluctuation, which have not been fully investigated before. We found that the classical and quantum models have different critical exponents and thus have different universality classes. We also briefly discuss the effects of the random field.

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