arXiv subjects

Parongama Sen

Publications and source records attributed to Parongama Sen.

At least 19 recordsLinked to original sources

arXiv2026

Persistence probability based dynamics and phase diagrams in biased q-voter models

Persistence probability in opinion dynamics models estimates the tendency of the agents not to change their initial opinion till the present time. Here we consider two nonlinear q-voter models with binary opinions, where the dynamics are governed by a biased choice when the q panel is not unanimous. The models are studied for different parameter ranges corresponding to the known stationary states. Mean field theory and numerical simulations are used to compute the persistence probability for the two types of opinion separately. The long time behavior in general is either a saturation or a decay that can be approximated by an exponential form, depending on the chosen parameters. Based on this, phase diagrams in the parameter space are presented for both the models. The regions in the phase diagrams indicate a strong correlation with the behavior of fixed points in the corresponding models, which is non-trivial as far as the persistence probability is concerned.

cond-mat.stat-mech↗

arXiv2026

Extending the Biswas--Chatterjee--Sen model with nonconformists and inflexibles

Originally, the Biswas--Chatterjee--Sen model was shown to exhibit an order/disorder phase transition for a sufficiently large number of negative interactions among actors. In this paper, the model is extended by the existence of anticonformists and inflexibles. Anticonformists are actors who define themselves in opposition to the group and may intentionally reject what most people accept, while inflexibles are those who do not change their opinions at all. Both discrete and continuous opinions are considered. With direct Monte Carlo simulations and mean-field calculations, we check the influence of fractions of anticonformists and inflexibles on the mean opinion in the system. With the mean-field calculations, we identify ranges of fractions of anticonformists where an ordered phase of the system is available. The results of the mean-field calculations perfectly match the results of the Monte Carlo simulations. We consider inflexibles adhered: (i) to extreme opinions; (ii) to specific opinions, and (iii) chosen independently of their initial opinion. For inflexibles adhered to specific and extreme opinions, they play a role of an effective bias suppressing the disordered phase in the system. The qualitative results of introducing anticonformists (inflexibles) in various ways (discrete/continuous opinions and annealed/quenched disorder) are roughly the same. However, for the model extended by inflexibles, we can observe a systematic shift of the mean order parameter to its higher values for quenched disorder compared with annealed disorder. On the other hand, for anticonformists modeled with a continuous space of opinions, we can observe a systematic shift of the mean order parameter to its higher values compared with the discrete space of opinions.

physics.soc-ph↗

arXiv2025

Analysing contrarian behaviour using nonlinear biased $q$-voter model

We investigate the role of contrarians in a recently proposed weighted-influence variant of the $q$-voter model. In this framework, non-unanimous influence groups affect the focal agent through weighted contributions governed by a bias parameter $p$. We extend this setting by introducing a fraction $\alpha$ ($\alpha> 0$) of contrarians, defined as agents who systematically oppose the prevailing influence irrespective of whether the group is unanimous or divided. Analytical mean-field calculations and Monte Carlo simulations reveal that the final states of the system are governed by simple phase boundaries: regions of positive and negative majority separated by the lines $p=1/2$ and $\alpha=1/2$, with equally-mixed states confined to these boundaries. While low contrarian densities are insufficient to overturn the bias, higher values of $\alpha$ systematically drive the system closer to a balanced coexistence of opinions, though exact parity is prevented by the presence of bias $p$. We further analyze the temporal relaxation of opinions and extract the characteristic timescales of convergence. Our findings highlight how contrarians, acting as structured non-conformists, can suppress consensus and maintain opinion diversity, while internal biases ultimately hinder a perfectly even split.

physics.soc-ph↗

arXiv2025

Virtual walks in the Ising model: finite time scaling

The dynamics of the spins in the Ising model are analyzed using a virtual walk scenario. The system is quenched from a very high temperature to a lower one using the Glauber scheme in one and two dimensions. A walk is associated with each spin which evolves according to the current state of the spin. The probability distribution of the displacement is calculated that shows a distinct change as the temperature is increased. The average displacement as a function of time shows a non-equilibrium region stretched over a much longer time interval compared to the bulk magnetization. Nevertheless, one can still detect a time dependent critical point determined by two different methods. In addition, we introduce a virtual walk constructed from the local energy of individual spins. Finite time scaling of the different quantities estimated in two dimensions show excellent consistency with the values of the known critical exponents.

cond-mat.stat-mech↗

arXiv2025

Sociophysics models inspired by the Ising model

The Ising model, originally developed for understanding magnetic phase transitions, has become a cornerstone in the study of collective phenomena across diverse disciplines. In this review, we explore how Ising and Ising-like models have been successfully adapted to sociophysical systems, where binary-state agents mimic human decisions or opinions. By focusing on key areas such as opinion dynamics, financial markets, social segregation, game theory, language evolution, and epidemic spreading, we demonstrate how the models describing these phenomena, inspired by the Ising model, capture essential features of collective behavior, including phase transitions, consensus formation, criticality, and metastability. In particular, we emphasize the role of the dynamical rules of evolution in the different models that often converge back to Ising-like universality. We end by outlining the future directions in sociphysics research, highlighting the continued relevance of the Ising model in the analysis of complex social systems.

physics.soc-ph↗

arXiv2025

Forager with intermittent rest: Better for survival?

We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to $S$ steps without food. We introduce the concept of intermittent rest in the dynamics which allows the forager to rest with probability $p$ upon consumption of food. The parameter $p$ significantly affects the lifetime of the forager, showing that the intermittent rest can be beneficial for the forager for chosen parameter values. The study of various other quantities reveals interesting scaling behavior with $p$ and also departure from usual diffusive behavior for $0.5 < p < 1$. In addition to numerical simulations, the problem has been studied with analytical approach in one dimension and the results up to $p < 0.5$ agree with the numerical ones to a large extent.

cond-mat.stat-mech↗

arXiv2025

Effect of presence of rigid impurities in a system of annihilating domain walls with dynamic bias

The dynamics of interacting domain walls, regarded as a system of particles which are biased to move towards their nearest neighbours and annihilate when they meet, have been studied in the recent past. We study the effect of the presence of a fraction $r$ of quenched impurities (which act as rigid walkers) on the dynamics. Here, in case two domain walls or one impurity and one domain wall happen to be on the same site, both get simultaneously annihilated. It is found that for any non-zero value of $r$, the dynamical behaviour changes as the surviving fraction of particles $\rho(t)$ attains a constant value. $\rho(t)t^\alpha $ shows a universal behaviour when plotted against $r^\beta t$ with $\alpha, \beta$ values depending on whether the particles are rigid or nonrigid. Also, the values differ for the biased and unbiased cases. The time scale associated with the particle decay obtained in several ways shows that it varies with $r$ in a power law manner with a universal exponent.

cond-mat.stat-mech↗

arXiv2025

Modeling biases in binary decision-making within the generalized nonlinear q-voter model

Collective decision-making is a process by which a group of individuals determines a shared outcome that shapes societal dynamics; from innovation diffusion to organizational choices. A common approach to model these processes is using binary dynamics, where the choices are reduced to two alternatives. One of the most popular models in this context is the $q$-voter model, which assumes that opinion changes are driven by peer pressure from a unanimous group. However, real-world decisions are also shaped by prior personal choices and external influences, such as mass media, which introduce biases that can favor certain options over others. To address this, we propose a generalized $q$-voter model that incorporates these biases. In our model, when the influence group is not unanimous, the probability that an individual changes its opinion depends on its current state, breaking the symmetry between opinions. In limiting cases, our model recovers both the original $q$-voter model and several recently introduced modifications of the $q$-voter model, while extending the framework to capture a broader range of scenarios. We analyze the model on a complete graph using analytical methods and Monte Carlo simulations. Our results highlight two key findings: (1) for larger influence groups ($q>3$), a phase emerges where both adopted and partially adopted states coexist, (2) in small systems, greater initial support for an opinion does not necessarily increase its likelihood of widespread adoption, as reflected in the unique form of the exit probability. These results point to one of the key issues in social science, the importance of group size in collective action.

physics.soc-ph↗

arXiv2024

Biswas-Chatterjee-Sen kinetic exchange opinion model for two connected groups

We consider a kinetic model of opinion dynamics known as the Biswas-Chatterjee-Sen model with a modular interaction structure. The system consists of two groups of agents that feature more frequent interactions within each group and rarer interactions between agents of different groups. We use the mean-field analytical approximation to determine that aside from previously known ordered and disordered states, a new antisymmetric ordered state is stable, where each group has an opposite dominant opinion. The limits of system interaction strength and noise for the stability of such a state are determined, with a discontinuous transition from an antisymmetric to a symmetric state happening if thresholds are exceeded. The results of numerical agent-based simulations confirm our analytical predictions and show that the critical values of noise and interaction strength are predicted with good accuracy.

physics.soc-ph↗

arXiv2024

Kinetic exchange opinion dynamics for the battleground-states in the 2024 US presidential elections

The strongly polarizing political discourse in the U. S. implies that a small minority of the population, determining the outcome of the presidential elections in a few so called battleground-states, also determines the outcome of the overall election. Given the almost equal distributions of the electoral college members in the so-called blue and red states, the members elected from these battleground states would determine the election results. We build a kinetic exchange opinion model that takes into account the dynamical nature of the opinions of the individuals in the battleground states and the already determined core voters of the non-battleground states. In a fully connected graph, we consider the interaction among the population in the battleground states while the agents in the non-battleground states are assumed to have fixed opinions. We provide the analytical results and numerical simulations using realistic parameters from the opinion poll of the previous election's data. Counter-intuitively, a more noisy environment predicts a higher chance of the Democrats' win.

physics.soc-ph↗

arXiv2024

On interactive anisotropic walks in two dimensions generated from a three state opinion dynamics model

A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. Here, the mapping is done in such a way that the walk is directed along the Y-axis while it can move either way along the X-axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power law behaviour, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents.

cond-mat.stat-mech↗

arXiv2024

Social Influence and Consensus Building: Introducing a q-Voter Model with Weighted Influence

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the best of our knowledge. When the bias is neutral, the model is reduced to a mean-field voter model. We analyze the behavior and steady states of the system, identifying three distinct regimes based on the bias level: one favoring negative opinions, one favoring positive opinions, and a neutral case. In large systems, the equilibrium properties become independent of the size of the group, indicating that only the bias influences the final outcome. However, for small groups, the time to reach equilibrium depends on the size of the group. Our results show that even a small initial bias leads to a consensus where all agents eventually share the same opinion when the bias is not neutral. The system exhibits universal behavior, with critical slowing down occurring near the neutral bias point, marking it as a critical dynamical threshold. The time required to reach consensus scales logarithmically when the bias is non-neutral and linearly when it is neutral. Although short-term dynamics depends on group size for small groups, long-term behavior is governed solely by the bias.

physics.soc-ph↗

arXiv2024

Virtual walks and phase transitions in two dimensional BChS model with extreme switches

We have studied a walk in a one-dimensional virtual space corresponding to an extended version of the three-state BChS model of opinion formation, originally proposed in Physica A {\bf 391}, 3257 (2012), in which the agents are located on a two dimensional lattice. The opinions are designated by the values $\pm1$ and zero. Here we also consider switches between the extreme states $\pm 1$. The model involves two noise parameters representing the fraction of negative interactions $p$ and the probability of extreme switch denoted by $q$. The study shows that the nature of the walks changes drastically as the noise parameters exceed certain threshold values. The order-disorder phase transitions are independently obtained using the finite size scaling method showing that these threshold values are indeed consistent with those values of the parameters where a phase transition exists. The criticality is found to be Ising-like even when extreme switches are allowed. A new critical exponent associated with the probability distribution of the displacement is also obtained independent of the values of the critical parameters. The nature of the walks is compared to similar virtual walks studied earlier.

cond-mat.stat-mech↗

arXiv2023

Avalanche shapes in fiber bundle model

We study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) the quasi-static loading, and (ii) loading by a discrete amount. In the quasi-static loading, where the load is increased by the minimum amount needed to initiate an avalanche, the temporal shapes of avalanches are asymmetric away from the critical point and become symmetric as the critical point is approached. A measure of asymmetry follows a universal form $A\sim (σ-σ_c)^θ$, with $θ\approx 0.25$, where $σ$ is the load per fiber and $σ_c$ is the critical load per fiber. This behavior is independent of the disorder present in the system in terms of the individual failure threshold values. Thus it is possible to use this asymmetry measure as a precursor to imminent failure. For the case of discrete loading, the load is always increased by a fixed amount. The dynamics of the model in this case can be solved in the mean field limit. It shows that the avalanche shapes always remain asymmetric. We also present a variable range load sharing version of this case, where the results remain qualitatively similar.

cond-mat.stat-mech↗

arXiv2023

Social dynamics through kinetic exchange: The BChS model

This review presents an overview of the current research in kinetic exchange models for opinion formation in a society. The review begins with a brief introduction to previous models and subsequently provides an in-depth discussion of the progress achieved in the Biswas-Chatterjee-Sen model proposed in 2012, also known as the BChS model in some later research publications. The unique feature of the model is its inclusion of negative interaction between agents. The review covers various topics, including phase transitions between different opinion states, critical behavior dependent on various parameters, and applications in realistic scenarios such as the United States presidential election and Brexit.

physics.soc-ph↗

arXiv2023

Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches

We investigate the non-equilibrium dynamics of a three state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter $q$. The mean field dynamical equations are derived and analysed for any $q$. The fate of the system under the evolutionary rules used in \cite{BCS} shows that it is dependent on the value of $q$ and the initial state in general. For $q=1$, which allows the extreme switches maximally, a quasi-conservation in the dynamics is obtained which renders it equivalent to the voter model. For general $q$ values, a "frozen" disordered fixed point is obtained which acts as an attractor for all initially disordered states. For other initial states, the order parameter grows with time $t$ as $\exp[α(q) t]$ where $α= \frac{1-q}{3-q}$ for $q\neq 1$ and follows a power law behaviour for $q=1$. Numerical simulations using a fully connected agent based model provide additional results like the system size dependence of the exit probability and consensus times that further accentuate the different behaviour of the model for $q=1$ and $q\neq 1$. The results are compared with the non-equilibrium phenomena in other well known dynamical systems.

cond-mat.stat-mech↗

arXiv2022

Opinion formation models with extreme switches and disorder: critical behaviour and dynamics

In a three state kinetic exchange opinion formation model, the effect of extreme switches was considered in a recent paper. In the present work, we study the same model with disorder. Here disorder implies that negative interactions may occur with a probability $p$. In absence of extreme switches, the known critical point is at $p_c =1/4$ in the mean field model. With a nonzero value of $q$ that denotes the probability of such switches, the critical point is found to occur at $ p = \frac{1-q}{4}$ where the order parameter vanishes with a universal value of the exponent $β=1/2$. Stability analysis of initially ordered states near the phase boundary reveals the exponential growth/decay of the order parameter in the ordered/disordered phase with a timescale diverging with exponent $1$. The fully ordered state also relaxes exponentially to its equilibrium value with a similar behaviour of the associated timescale. Exactly at the critical points, the order parameter shows a power law decay with time with exponent $1/2$. Although the critical behaviour remains mean field like, the system behaves more like a two state model as $q \to 1$. At $q=1$ the model behaves like a binary voter model with random flipping occurring with probability $p$.

cond-mat.stat-mech↗

arXiv2022

$A+A \rightarrow \emptyset $ model with a bias towards nearest neighbor

We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $ε$ $(0 \leq ε\leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $ε=0$ to the mean-field value of unity for any non-zero $ε$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z} f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.

cond-mat.stat-mech↗