arXiv subjects

Swarnajit Chatterjee

Publications and source records attributed to Swarnajit Chatterjee.

18 recordsLinked to original sources

arXiv2026

Stability and breakdown of chiral motion in non-reciprocal flocking

We study a two-species Vicsek model with intra-species alignment and asymmetric inter-species couplings, where one species aligns with the other while the latter anti-aligns. Motivated by recent results showing that globally coherent chiral motion is not a generic large-scale state of finite-range nonreciprocal flocking, we ask whether a chiral state can nevertheless be stabilized in the discrete-time, metric, nonreciprocal two-species Vicsek model, and if so, under what conditions. For equal populations and motilities, we find that the global chiral state is a long-lived finite-time state rather than an asymptotically stable phase at nonzero motility. Its breaking time increases rapidly as the self-propulsion speed is reduced or the strength of the nonreciprocal coupling is enhanced, explaining why systems with very low motility can appear stably chiral over conventional simulation timescales. This finite-time chiral regime is further limited to high-density systems and to system sizes that are small relative to the interaction range. Within this window, we also find that chirality appears primarily when aligning interactions dominate over anti-alignment, whereas stronger anti-alignment leads to species segregation and suppresses chirality. Conversely, introducing species asymmetry through population imbalance drives transitions from the finite-time chiral regime to porous parallel-flocking or anti-parallel-flocking liquids; motility imbalance induces asynchronous oscillations and, in extreme cases, leads to segregation into moving clusters of the faster species within a more dispersed background of slower particles. Overall, these results indicate that chirality in the nonreciprocal two-species Vicsek model arises within a restricted regime set by density, motility, inter-species coupling, and system size, rather than being a generic outcome of nonreciprocal interactions.

cond-mat.stat-mech↗

arXiv2026

Field-controlled interfacial transport and pinning in an active spin system

Field control provides a practical route to programmable active matter, yet how weak fields modify non-equilibrium coexistence and interfaces remains unclear. To address this, we study a minimal flocking model of active Potts particles coupled to an external field and show that even weak fields can reconfigure phase behavior and interfacial dynamics. For a homogeneous unidirectional field, the flocking phase is reshaped: the coexistence regime between an apolar gas and a polar liquid is replaced by a phase separation between two field-aligned polar phases: a low-density, weakly polarized background and a high-density, strongly polarized band, both moving along the field. When the system forms a dense longitudinal lane oriented transverse to the field, it executes a slow treadmilling motion against the field, driven by the weakly polarized background. If the system is divided into regions with opposite field directions, particles accumulate at the interface, leading to field-induced interface pinning with flocks performing back-and-forth oscillatory motion. In the presence of quenched random field orientations, this pinning favors a disordered state in which global order diminishes with increasing system size, consistent with Imry-Ma arguments, while the quenched disorder smoothens sharp first-order signatures, in line with the Aizenman-Wehr theorem, with activity modifying the scaling. A coarse-grained hydrodynamic theory supports these observations and is consistent with microscopic simulations.

cond-mat.soft↗

arXiv2025

Stability of discrete-symmetry flocks: sandwich state, traveling domains and motility-induced pinning

Polar flocks in discrete active systems are often assumed to be robust, yet recent studies reveal their fragility under both imposed and spontaneous fluctuations. Here, we revisit the four-state active Potts model (APM) and show that its globally ordered phase is metastable across a broad swath of parameter space. Small counter-propagating droplets disrupt the flocking phase by inducing a persistent sandwich state, where the droplet-induced opposite-polarity lane remains embedded within the original flock, particularly pronounced at low noise, influenced by spatial anisotropy. In contrast, small transversely propagating droplets, when introduced into the flock, can trigger complete phase reversal due to their alignment orthogonal to the dominant flow and their enhanced persistence. At low diffusion and strong self-propulsion, such transverse droplets also emerge spontaneously, fragmenting the flock into multiple traveling domains and giving rise to a short-range order (SRO) regime. We further identify a motility-induced pinning (MIP) transition in small diffusion and low-temperature regimes when particles of opposite polarity interact, flip their state, hop, and pin an interface. Our comprehensive phase diagrams, encompassing full reversal, sandwich coexistence, stripe bands, SRO, and MIP, delineate how thermal fluctuations, self-propulsion strength, and diffusion govern flock stability in discrete active matter systems.

cond-mat.soft↗

arXiv2025

Stability of flocking in the reciprocal two-species Vicsek model: Effects of relative population, motility, and noise

Natural flocks need to cope with various forms of heterogeneities, for instance, their composition, motility, interaction, or environmental factors. Here, we study the effects of such heterogeneities on the flocking dynamics of the reciprocal two-species Vicsek model [Phys. Rev. E 107, 024607 (2023)], which comprises two groups of self-propelled agents with anti-aligning inter-species interactions and exhibits either parallel or anti-parallel flocking states. The parallel and anti-parallel flocking states vanish upon reducing the size of one group, and the system transitions to a single-species flock of the majority species. At sufficiently low noise (or high density), the minority species can exhibit collective behavior, anti-aligning with the liquid state of the majority species. Unequal self-propulsion speeds of the two species strongly encourage anti-parallel flocking over parallel flocking. However, when activity landscapes with region-dependent motilities are introduced, parallel flocking is retained if the faster region is given more space, highlighting the role of environmental constraints. Under noise heterogeneity, the colder species (subjected to lower noise) attain higher band velocity compared to the hotter one, temporarily disrupting any parallel flocking, which is subsequently restored. These findings collectively reveal how different forms of heterogeneity, both intrinsic and environmental, can qualitatively reshape flocking behavior in this class of reciprocal two-species models.

cond-mat.stat-mech↗

arXiv2024

Emergent complex phases in a discrete flocking model with reciprocal and non-reciprocal interactions

There is growing interest in multi-species active matter systems with reciprocal and non-reciprocal interactions. While such interactions have been explored in continuous symmetry models, less is known about multi-species discrete-symmetry systems. To address this, we study the two-species active Ising model (TSAIM), a discrete counterpart of the two-species Vicsek model. Our investigation explores both inter-species reciprocal and non-reciprocal interactions, along with the possibility of species interconversion. In the reciprocal TSAIM, we observe the emergence of a high-density parallel flocking state, a feature not seen in previous flocking models. With species interconversion, the TSAIM corresponds to an active extension of the Ashkin-Teller model and exhibits rich state diagrams. In the non-reciprocal TSAIM, a run-and-chase dynamics emerge. We also find that the system is metastable due to droplet excitation and exhibits spontaneous motility-induced interface pinning. A hydrodynamic theory validates our numerical simulations and confirms the phase diagrams.

cond-mat.stat-mech↗

arXiv2024

Ordering kinetics in the active Ising model

We undertake a numerical study of the ordering kinetics in the two-dimensional ($2d$) active Ising model (AIM), a discrete flocking model with a conserved density field coupled to a non-conserved magnetization field. We find that for a quench into the liquid-gas coexistence region and in the ordered liquid region, the characteristic length scale of both the density and magnetization domains follows the Lifshitz-Cahn-Allen (LCA) growth law: $R(t) \sim t^{1/2}$, consistent with the growth law of passive systems with scalar order parameter and non-conserved dynamics. The system morphology is analyzed with the two-point correlation function and its Fourier transform, the structure factor, which conforms to the well-known Porod's law, a manifestation of the coarsening of compact domains with smooth boundaries. We also find the domain growth exponent unaffected by different noise strengths and self-propulsion velocities of the active particles. However, transverse diffusion is found to play the most significant role in the growth kinetics of the AIM. We extract the same growth exponent by solving the hydrodynamic equations of the AIM.

cond-mat.stat-mech↗

arXiv2023

Consequence of anisotropy on flocking: the discretized Vicsek model

We numerically study a discretized Vicsek model (DVM) with particles orienting in $q$ possible orientations in two dimensions. The study probes the significance of anisotropic orientation and microscopic interaction on the macroscopic behavior. The DVM is an off-lattice flocking model like the active clock model [ACM; EPL {\bf 138}, 41001 (2022)] but the dynamical rules of particle alignment and movement are inspired by the prototypical Vicsek model (VM). The DVM shows qualitatively similar properties as the ACM for intermediate noise strength where a transition from macrophase to microphase separation of the coexistence region is observed as $q$ is increased. But for small $q$ and noise strength, the liquid phase appearing in the ACM at low temperatures is replaced in the DVM by a configuration of multiple clusters with different polarization which does not exhibit any long-range order. We find that the dynamical rules have a profound influence on the overarching features of the flocking phase. We further identify the metastability of the ordered liquid phase subjected to a perturbation.

cond-mat.stat-mech↗

arXiv2022

Jamming and flocking in the restricted active Potts model

We study the active Potts model with either site occupancy restriction or on-site repulsion to explore jamming and kinetic arrest in a flocking model. The incorporation of such volume exclusion features leads to a surprisingly rich variety of self-organized spatial patterns. While bands and lanes of moving particles commonly occur without or under weak volume exclusion, strong volume exclusion along with low temperature, high activity, and large particle density facilitates jams due to motility-induced phase separation. Through several phase diagrams, we identify the phase boundaries separating the jammed and free-flowing phases and study the transition between these phases which provide us with both qualitative and quantitative predictions of how jamming might be delayed or dissolved. We further formulate and analyze a hydrodynamic theory for the restricted APM which predicts various features of the microscopic model.

cond-mat.stat-mech↗

arXiv2022

Flocking of two unfriendly species: The two-species Vicsek model

We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to antialign with the other. The model shows a flocking transition that is reminiscent of the original Vicsek model: it has a liquid-gas phase transition and displays micro-phase-separation in the coexistence region where multiple dense liquid bands propagate in a gaseous background. The interesting features of the TSVM are the existence of two kinds of bands, one composed of mainly A particles and one mainly of B particles, the appearance of two dynamical states in the coexistence region: the PF (parallel flocking) state in which all bands of the two species propagate in the same direction, and the APF (antiparallel flocking) state in which the bands of species A and species B move in opposite directions. When PF and APF states exist in the low-density part of the coexistence region they perform stochastic transitions from one to the other. The system size dependence of the transition frequency and dwell times show a pronounced crossover that is determined by the ratio of the band width and the longitudinal system size. Our work paves the way for studying multispecies flocking models with heterogeneous alignment interactions.

cond-mat.stat-mech↗

arXiv2022

Polar flocks with discretized directions: the active clock model approaching the Vicsek model

We consider the off-lattice two-dimensional $q$-state active clock model (ACM) as a natural discretization of the Vicsek model (VM) describing flocking. The ACM consists of particles able to move in the plane in a discrete set of $q$ equidistant angular directions, as in the active Potts model (APM), with an alignment interaction inspired by the ferromagnetic equilibrium clock model. We find that for a small number of directions, the flocking transition of the ACM has the same phenomenology as the APM, including macrophase separation and reorientation transition. For a larger number of directions, the flocking transition in the ACM becomes equivalent to the one of the VM and displays microphase separation and only transverse bands, i.e. no re-orientation transition. Concomitantly also the transition of the $q\to\infty$ limit of the ACM, the active XY model (AXYM), is in the same universality class as the VM. We also construct a coarse-grained hydrodynamic description for the ACM and AXYM akin to the VM.

cond-mat.stat-mech↗

arXiv2021

Active XY model on a substrate: Density fluctuations and phase ordering

We explore the generic long wavelength properties of an active XY model on a substrate, consisting of collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte-Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it shows phase ordering which is generically either logarithmically stronger than the conventional quasi long range order (QLRO) found in its equilibrium limit, together with "miniscule number fluctuations", or logarithmically weaker than QLRO along with "giant number fluctuations", showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short range phase-order are found, characterized by the presence or absence of stable clusters of finite sizes.

cond-mat.stat-mech↗

arXiv2021

Mobility-induced order in active XY spins on a substrate

We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are distinguished by generalized quasi-long range (QLRO) orientational order logarithmically stronger or weaker than the well-known QLRO in equilibrium, together with miniscule (i.e., hyperuniform) or giant number fluctuations, respectively. This illustrates a direct correspondence between the two. The scaling of both phase and density fluctuations in the stable phase-ordered states is nonuniversal: they depend on the nonlinear dynamical couplings. For other parameters, it has no stable uniformly ordered phase. Our model, a theory for active spinners, provides a minimal framework for wide-ranging systems, e.g., active superfluids on substrates, synchronization of oscillators, active carpets of cilia and bacterial flagella and active membranes.

cond-mat.stat-mech↗

arXiv2020

SEIRD model to study the asymptomatic growth during COVID-19 pandemic in India

According to the current perception, symptomatic, presymptomatic, and asymptomatic infectious persons can infect the healthy population susceptible to the SARS-Cov-2. More importantly, various reports indicate that the number of asymptomatic cases can be several-fold higher than the reported symptomatic cases. In this article, we take the reported cases in India and various states within the country till September 1, as the specimen to understand the progression of the COVID-19. Employing a modified SEIRD model, we predict the spread of COVID-19 by the symptomatic as well as asymptomatic infectious population. Considering reported infection primarily due to symptomatic we compare the model predicted results with the available data to estimate the dynamics of the asymptomatically infected population. Our data indicate that in the absence of the asymptomatic infectious population, the number of symptomatic cases would have been much less. Therefore, the current progress of the symptomatic infection can be reduced by quarantining the asymptomatically infectious population via extensive or random testing. This study is motivated strictly towards academic pursuit; this theoretical investigation is not meant for influencing policy decisions or public health practices.

q-bio.PE↗

arXiv2020

Flocking with a $q$-fold discrete symmetry: band-to-lane transition in the active Potts model

We study the $q$-state active Potts model (APM) on a two-dimensional lattice in which self-propelled particles have $q$ internal states corresponding to the $q$ directions of motion. A local alignment rule inspired by the ferromagnetic $q$-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to a collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory of the model, compute the phase diagrams of the APM for $q=4$ and $q=6$ and explore the flocking dynamics in the region, in which the high-density (polar liquid) phase coexists with the low-density (gas) phase and forms a fluctuating stripe of coherently moving particles. As a function of the particle self-propulsion velocity, a novel reorientation transition of the phase-separated profiles from transversal band motion to longitudinal lane formation is revealed, which is absent in the Vicsek model and APM for $q=2$ (active Ising model). The origin of this reorientation transition is obtained via a stability analysis: for large velocities, the transverse diffusion constant approaches zero and stabilizes lanes. Finally, we perform microscopic simulations that corroborate our analytical predictions about the flocking and reorientation transitions and validate the phase diagrams of the APM.

cond-mat.stat-mech↗

arXiv2020

Ordering kinetics in q-state random-bond clock model: Role of Vortices and Interfaces

In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $ε$. Effect of $ε$ on the non-equilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long range ordered (QLRO, $T_c^2 < T < T_c^1$) regime and long-range ordered (LRO, $T<T_c^2$) regime at temperature $T$. We report that the dynamical scaling of the correlation function and structure factor are independent of $ε$ and the presence of quenched disorder slows down domain coarsening. Coarsening dynamics in both LRO and QLRO regimes are further characterized by power-law growth with disorder-dependent exponents within our simulation time scales. The growth exponents in the LRO regime decreases from 0.5 in the pure case to 0.22 in the maximum disordered case, whereas the corresponding change in the QLRO regime happens from 0.45 to 0.38. We further explored the coarsening dynamics in the bond-diluted clock model and in both the models, the effect of the disorder is more significant for the quench in the LRO regime compared to the QLRO regime.

cond-mat.stat-mech↗

arXiv2020

Flocking and reorientation transition in the 4-state active Potts model

We study the active 4-state Potts model (APM) on the square lattice in which active particles have four internal states corresponding to the four directions of motion. A local alignment rule inspired by the ferromagnetic 4-state Potts model and self-propulsion via biased diffusion according to the internal particle states leads to flocking at high densities and low noise. We compute the phase diagram of the APM and explore the flocking dynamics in the region, in which the high-density (liquid) phase coexists with the low-density (gas) phase and forms a fluctuating band of coherently moving particles. As a function of the particle self-propulsion velocity, a novel reorientation transition of the phase-separated profiles from transversal to longitudinal band motion is revealed, which is absent in the Vicsek model and the active Ising model. We further construct a coarse-grained hydrodynamic description of the model which validates the results for the microscopic model.

cond-mat.stat-mech↗

arXiv2018

Ordering kinetics in q-state clock model: scaling properties and growth laws

We present a comprehensive Monte Carlo study of the ordering kinetics in the $d=2$ ferromagnetic $q$-state clock model with nonconserved Glauber dynamics. In agreement with previous studies we find that $q \geqslant 5$ is characterized by two phase transitions occurring at temperatures $T_{c}^1$ and $T_{c}^2$ ($T_{c}^2<T_{c}^1$). Phase ordering kinetics is then investigated by rapidly quenching the system in two phases, in the quasi-long range ordered phase (QLRO) where $T_{c}^2<T<T_{c}^1$ and in the long-range ordered phase (LRO) where $T<T_{c}^2$; $T$ being the quench temperature. Our numerical data for equal time spatial correlation function $C(\textbf{r},t)$ and structure factor $S(k,t)$ support dynamical scaling. Quench in the LRO regime is characterized by a crossover from a preasymptotic growth driven by the annealing of both vortices and interfaces to an interface driven growth at the asymptotic regime with growth exponent $n\simeq 0.5$. In the QLRO quench regime, domains coarsen mainly via annihilation of point defects and our length scale data for $q$ = 9, 12, and 20 suggests a $R(t) \sim (t/\ln t)^{1/2}$ growth law for the $q$-state clock model in the QLRO phase.

cond-mat.stat-mech↗

arXiv2017

Ordering Kinetics in the Random Bond XY Model

We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with non-conserved kinetics. The presence of quenched disorder slows down domain growth in d = 2; 3. In d = 2, we observe power-law growth with a disorder-dependent exponent on the time-scales of our simulation. In d = 3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality.

cond-mat.stat-mech↗