arXiv subjects

Amit Pradhan

Publications and source records attributed to Amit Pradhan.

6 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

Diffusive-to-Ballistic transition in a Persistent Random Walk

We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim t^{-\alpha}$ and show that the system undergoes a transition at $\alpha=1$, separating a super-diffusive regime for $\alpha<1$ from ballistic regime for $\alpha \geq 1$. Using the results for velocity correlations and persistence statistics, together with finite time scaling of the Binder cumulant and displacement fluctuations, we characterize the transition and its properties in detail. We further argue that the transition is not limited to the power law form, but can also arise for several other time dependent reversal probabilities satisfying the same criterion. The transition persists in arbitrary spatial dimensions provided isotropy of the velocity space is preserved.

cond-mat.stat-mech↗

arXiv2026

Generalized BChS Model with Group Interactions: Shift in the Critical Point and Mean-Field Ising Universality

We introduce a generalized version of the Biswas-Chatterjee-Sen (BChS) model \cite{Biswas} with group interactions of size $q$, extending the original pairwise interaction dynamics. Within a mean-field framework, we derive an exact expression for the critical noise $p_c(q)$, showing that it increases monotonically with $q$ and approaches $1/2$ in the large-$q$ limit, consistent with a Gaussian approximation. Despite this shift in the phase boundary, the critical behavior remains unchanged across all $q$: the order parameter scales as $(p_c(q)-p)^{1/2}$, and the relaxation timescale diverges as $|p-p_c(q)|^{-1}$, identical to the original BChS model \cite{Biswas}. Finite-size scaling of the Binder cumulant, order parameter, and its fluctuations confirm that the system belongs to the mean-field Ising universality class for all $q$. Our results demonstrate that higher-order interactions modify the location of the transition without altering its universality class.

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↗