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Chiu Fan Lee

Publications and source records attributed to Chiu Fan Lee.

At least 19 recordsLinked to original sources
arXiv2026

Hydrodynamics, Renormalization Group, and Universality Classes Far from Equilibrium

Universality is one of the central organising principles of modern physics, explaining why systems with vastly different microscopic constituents can exhibit identical large-scale behaviour. While the classification of equilibrium critical phenomena through hydrodynamics and the renormalization group (RG) is now well established, our understanding of universality far from equilibrium remains far less developed. In recent years, however, rapid progress - driven in large part by developments in active and living matter - has uncovered a growing range of genuinely nonequilibrium universality classes (UCs) with no equilibrium counterparts. In this review, we present a pedagogical and unified introduction to hydrodynamic and RG approaches to nonequilibrium many-body systems. We first show how hydrodynamic theories can be systematically constructed from symmetry and conservation laws alone. We then introduce perturbative dynamic RG methods and demonstrate how hydrodynamic theories are organised into distinct UCs according to their scaling behaviour. Building on these foundations, we review the diverse nonequilibrium UCs uncovered since 2015, while emphasizing the conceptual connections and unifying physical principles underlying their emergence. We conclude by discussing open theoretical and experimental challenges for the field.

cond-mat.soft↗
arXiv2025

Diversity of critical phenomena in the ordered phase of polar active fluids

We present a comprehensive analytical linear stability analysis of the Toner-Tu model for polar active fluids in the ordered phase. Our results provide exact instability criteria and demonstrate that all generic hydrodynamic instabilities fall into two fundamental categories, distinguished by their scaling with the wavevector magnitude. By applying a general criticality condition, we show that each instability can give rise to a critical point by fine-tuning only two parameters. We identify four previously unreported critical points of the Toner-Tu model, two of which already display nonequilibrium critical behavior that extends beyond known universality classes at the linear level. We further construct explicit hydrodynamic models that realize each newly identified critical point, establishing their physical attainability and providing concrete targets for future renormalization-group analyses and microscopic model studies. Altogether, our framework offers a unified theoretical foundation and a practical roadmap for the systematic discovery of new universality classes in active matter.

cond-mat.soft↗
arXiv2025

Vertex Model Mechanics Explain the Emergence of Centroidal Voronoi Tiling in Epithelia

Epithelia are confluent cell layers that self-organize into polygonal networks whose geometry encodes their mechanical state. A principal driver is the tunable contractility of the actomyosin cortex, which links cell-junction tension to tissue architecture. Notably, epithelial tilings frequently resemble centroidal Voronoi tessellations (CVTs), yet the physical origin of this resemblance has remained unclear. Here, using a minimal vertex model that relates cell shape to a mechanical energy, we show that CVT-like patterns arise naturally in the solid (rigid) regime of tissues. Analytical theory reveals that isotropic strain minimization drives cell centroids toward Voronoi configurations, a result we corroborate with a analytical mean-field formulation of the vertex model. We further demonstrate that physiologically relevant perturbations -- such as cyclic stretch -- shift tissues into distinct, geometrically disordered CVT states, and that these shifts provide quantitative, image-based readouts of mechanical state. Together, our results identify a mechanical origin for CVT-like organization in epithelia and establish a geometric framework that infers tissue stresses directly from morphology, offering broadly applicable metrics for assessing rigidity and remodeling in living tissues.

cond-mat.soft↗
arXiv2025

Universal behavior at the Lifshitz Points of an active Malthusian Ising model

Lifshitz points (LPs) are multicritical points where ordered, disordered, and patterned phases meet. Originally studied in equilibrium magnetic systems, LPs have since been identified in soft matter and even cosmological settings. Their role in active, living matter, however, remains entirely unexplored. Here we address this gap by introducing and analyzing LPs in the Active Malthusian Ising Model (AMIM) -- a minimal model of living matter that incorporates motility together with birth-death dynamics. Despite its simplicity, the AMIM provides direct experimental relevance. We show that the system generically exhibits two distinct LPs and elucidate their universal behavior using a dynamic renormalization group analysis with the $ε$-expansion method at one loop. Our results yield testable predictions for future simulations and experiments, establishing LPs as a fertile testing ground for novel physics in active matter.

cond-mat.soft↗
arXiv2025

Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks

We study the hydrodynamic behavior of two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. We show that, in the absence of fluctuations, such systems generically form a ``time cholesteric", in which the velocity of the entire system rotates uniformly at a fixed frequency b. Fluctuations about this state belong to the universality class of (2+1)-Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order in the hydrodynamic limit. We then show that, in the limit of weak chirality, the hydrodynamics of a system with reasonable size is expected to governed by the linear regime of the KPZ equation, exhibiting quasi-long-ranged orientational order. Our predictions for the velocity and number density correlations are testable in both simulations and experiments.

cond-mat.soft↗
arXiv2025

The Order-disorder Transition in Incompressible Polar Active Fluids with an Easy Axis

Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar active fluid that preferentially flows along a particular axis induced by the anisotropy of the medium. We then study its critical behavior at the order-disorder transition in which the symmetry between ``forward" and ``back" along the special axis is spontaneously broken. We obtain the critical static and dynamic exponents, mean velocity, and two point correlation functions exactly in three dimensions, and to two-loop level in two dimensions, by mapping our class of systems to the equilibrium Ising model with dipolar interactions.

cond-mat.soft↗
arXiv2025

Only the Ambidextrous Can Flock: Two-dimensional Chiral Malthusian Flocks, Time Cholesterics, and the KPZ Equation

We study two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. In the absence of fluctuations, these form a ``time cholesteric", in which the velocity rotates uniformly in time at a fixed frequency. Fluctuations are described by the (2+1)-Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order. For weak chirality, the system is in the linear regime of the KPZ equation for a wide range of length scales, over which it exhibits quasi-long-ranged orientational order. Our predictions for velocity and density correlations are testable in both simulations and experiments.

cond-mat.soft↗
arXiv2025

New universality classes govern the critical and multicritical behavior of an active Ising model

The Ising model is one of the most well known models in statistical physics, with its critical behavior governed by the Wilson-Fisher universality class (UC). When active motility is incorporated into the Ising model by, e.g., dictating that the spins' directional movements follow their orientations, the spin number density necessarily constitutes a soft mode in the hydrodynamic description, and can therefore modify the scaling behavior of the system. Here, we show that this is indeed the case in a critical active Ising model in which density can impede the system's collective motion. Specifically, we use a perturbative dynamic renormalization group method to the one-loop level to uncover three new UCs, one of which supersedes the Wilson-Fisher UC to become the generic UC that governs the critical behavior of the active Ising model.

cond-mat.stat-mech↗
arXiv2025

The inconvenient truth about flocks

We reanalyze the hydrodynamic theory of "flocks" that is, polar ordered "dry" active fluids in two dimensions. For "Malthusian" flocks, in which birth and death cause the density to relax quickly, thereby eliminating density as a hydrodynamic variable, we are able to obtain two exact scaling laws relating the three scaling exponents characterizing the long-distance properties of these systems. We also show that it is highly plausible that such flocks display long-range order in two dimensions. In addition, we demonstrate that for "immortal" flocks, in which the number of flockers is conserved, the extra non-linearities allowed by the presence of an extra slow variable (number density) make it impossible to obtain any exact scaling relations between the exponents. We thereby demonstrate that several past published claims of exact exponents for Malthusian and immortal flocks are all incorrect.

cond-mat.soft↗
arXiv2024

Can exact scaling exponents be obtained using the renormalization group? Affirmative evidence from incompressible polar active fluids

In active matter systems, non-Gaussian, exact scaling exponents have been claimed in a range of systems using perturbative renormalization group (RG) methods. This is unusual compared to equilibrium systems where non-Gaussian exponents can typically only be approximated, even using the exact (or functional/nonperturbative) renormalization group (ERG). Here, we perform an ERG analysis on the ordered phase of incompressible polar active fluids and find that the exact non-Gaussian exponents obtained previously using a perturbative RG method remain valid even in this nonperturbative setting. Furthermore, our ERG analysis elucidates the RG flow of this system and enables us to identify an active Goldstone regime with nontrivial, long-ranged scaling behavior for parallel and longitudinal fluctuations.

cond-mat.soft↗
arXiv2024

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

The Vicsek simulation model of flocking together with its theoretical treatment by Toner and Tu in 1995 were two foundational cornerstones of active matter physics. However, despite the field's tremendous progress, the actual universality class (UC) governing the scaling behavior of Viscek's "flocking" phase remains elusive. Here, we use nonperturbative, functional renormalization group methods to analyze, numerically and analytically, a simplified version of the Toner-Tu model, and uncover a novel UC with scaling exponents that agree remarkably well with the values obtained in a recent simulation study by Mahault et al. [Phys. Rev. Lett. 123, 218001 (2019)], in both two and three spatial dimensions. We therefore believe that there is strong evidence that the UC uncovered here describes Vicsek's flocking phase.

cond-mat.soft↗
arXiv2023

Active Jamming at Criticality

Jamming is ubiquitous in disordered systems, but the critical behavior of jammed solids subjected to active forces or thermal fluctuations remains elusive. In particular, while passive athermal jamming remains mean-field-like in two and three dimensions, diverse active matter systems exhibit anomalous scaling behavior in all physical dimensions. It is therefore natural to ask whether activity leads to anomalous scaling in jammed systems. Here, we use numerical and analytical methods to study systems of active, soft, frictionless spheres in two dimensions, and elucidate the universal scaling behavior that relates the excess coordination, active forces or temperature, and pressure close to the athermal jammed point. We show that active forces and thermal effects around the critical jammed state can again be captured by a mean-field picture, thus highlighting the distinct and crucial role of amorphous structure in active matter systems.

cond-mat.soft↗
arXiv2023

Nonequilibrium glass transitions in the spherical $p$-spin model with antisymmetric interactions

Our theoretical understanding of glassy dynamics is notoriously incomplete, and it is even more so when the glassy systems are driven out of equilibrium. An extreme way to drive a system out of equilibrium is to introduce nonequilibrium dynamics at the microscopic level, e.g., through active forcing of the constituent particles or by having nonreciprocal interactions among the particles. While glassy dynamics under active forcing has been studied by many, the latter nonequilibrium scenario has received little attention. Here, I study the glassy dynamics of the spherical $p$-spin model for $p\geq 3$ with antisymmetric interactions, which generalizes reciprocal interactions in 2-body interactions. The spherical $p$-spin model is an integral tool in the study of dynamical glass transition, and when antisymmetric interactions are added, I show analytically and numerically that glassy behavior is generically suppressed. Moreover, I obtain analytical expressions on the modified dynamical glass transition point and the Edward-Anderson parameter (i.e., the asymptotic plateau height value of the spin-spin correlation function) in the small driving limit.

cond-mat.soft↗
arXiv2023

Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks

We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the ``roughness" exponent $χ$ and anisotropy exponent $ζ$ that are extremely near the known exact results. This implies our prediction for the previously completely unknown dynamic exponent $z$ is quantitatively accurate.

cond-mat.soft↗
arXiv2023

Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies

Active matter is not only relevant to living matter and diverse nonequilibrium systems, but also constitutes a fertile ground for novel physics. Indeed, dynamic renormalization group (DRG) analyses have uncovered many new universality classes (UCs) in polar active fluids (PAFs) - an archetype of active matter systems. However, due to the inherent technical difficulties in the DRG methodology, almost all previous studies have been restricted to polar active fluids in the incompressible or infinitely compressible (i.e., Malthusian) limits, and, when the $ε$-expansion was used in conjunction, to the one-loop level. Here, we use functional renormalization group (FRG) methods to bypass some of these difficulties and unveil for the first time novel critical behavior in compressible polar active fluids, and calculate the corresponding critical exponents beyond the one-loop level. Specifically, we investigate the multicritical point of compressible PAFs, where the critical order-disorder transition coincides with critical phase separation. We first study the critical phenomenon using a DRG analysis and find that it is insufficient since two-loop effects are important to obtain a nontrivial correction to the scaling exponents. We then remedy this defect by using a FRG analysis. We find three novel universality classes and obtain their critical exponents, which we then use to show that at least two of these universality classes are out of equilibrium because they violate the fluctuation-dissipation relation.

cond-mat.soft↗
arXiv2023

Machine learning topological defects in confluent tissues

Active nematics is an emerging paradigm for characterising biological systems. One aspect of particularly intense focus is the role active nematic defects play in these systems, as they have been found to mediate a growing number of biological processes. Accurately detecting and classifying these defects in biological systems is, therefore, of vital importance to improving our understanding of such processes. While robust methods for defect detection exist for systems of elongated constituents, other systems, such as epithelial layers, are not well suited to such methods. Here, we address this problem by developing a convolutional neural network to detect and classify nematic defects in confluent cell layers. Crucially, our method is readily implementable on experimental images of cell layers and is specifically designed to be suitable for cells that are not rod-shaped. We demonstrate that our machine learning model outperforms current defect detection techniques and that this manifests itself in our method requiring less data to accurately capture defect properties. This could drastically improve the accuracy of experimental data interpretation whilst also reducing costs, advancing the study of nematic defects in biological systems.

cond-mat.soft↗
arXiv2023

Modeling growing confluent tissues using a lattice Boltzmann method: interface stability and fluctuations

Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are often limited by the size of systems that can be modeled. Here, we address this limitation by introducing a Lattice-Boltzmann method (LBM) for a growing system that is able to efficiently model hydrodynamic length-scales. The model incorporates a novel approach to describing the growing front of a tissue, which we use to investigate the dynamics of the interface of growing model tissues. We find that the interface grows with scaling in agreement with the Kardar-Parisi-Zhang (KPZ) universality class when growth in the system is bulk driven. Interestingly, we also find the emergence of a previously unreported hydrodynamic instability when proliferation is restricted to the tissue edge. We then develop an analytical theory to show that the instability arises due to a coupling between the number of cells actively proliferating and the position of the interface.

cond-mat.soft↗