arXiv subjects

Sara Oliver-Bonafoux

Publications and source records attributed to Sara Oliver-Bonafoux.

5 recordsLinked to original sources

arXiv2026

Barrier crossing in a two-state system: Effect of bias and stochastic fields

We study barrier crossing in a two-state system, namely the kinetic Ising model, in the presence of a weak bias field and spatially homogeneous, but time-dependent, Gaussian random fields. We find that the bias field determines the location of the dominant maxima of the probability distribution function of the magnetization, whereas the noise intensity controls their sharpness and stability of the distribution. A moderate stochastic field lowers the effective energy barrier and facilitates transitions between ordered states, while strong noise induces broad distributions and significant backflow, which reduces directional selectivity. Our results suggest that efficient barrier crossing requires a balanced combination of moderate stochastic driving and controlled bias.

cond-mat.stat-mech↗

arXiv2026

Numerical methods for quasi-stationary distributions

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its computation. The first is an iterative algorithm for solving the non-linear equation that defines the quasi-stationary distribution. We generalise this technique to accommodate general Markov stochastic processes, either with discrete or continuous state space, and with multiple absorbing states. The second is a Monte Carlo method with resetting, for which we propose a novel single-trajectory approach that uses the trajectory's own history to perform resets after absorption. In addition to these methodological contributions, we provide a detailed analysis of implementation aspects for both methods. We also compare their accuracy and efficiency across a range of examples. The results indicate that the iterative algorithm is generally the preferred choice for problems with simple boundaries, while the Monte Carlo approach is more suitable for problems with complex boundaries, where the implementation of the iterative algorithm is a challenging task.

cond-mat.stat-mech↗

arXiv2026

Stochastic field effects in a two-state system: symmetry breaking and symmetry restoring

We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability distribution as a function of temperature and field strength, and by computing the time required for the system to escape from a completely ordered state of the magnetization. We identify three distinct phases: a soft-paramagnetic phase, a soft-ferromagnetic phase and a bona-fide ferromagnetic phase. These soft phases display broad magnetization distributions that tend to limiting forms that remain finite in both height and width in the thermodynamic limit. The transition between the soft-paramagnetic and soft-ferromagnetic phases is a noise-induced transition and, for small field amplitudes, occurs at the critical temperature of the field-free Ising model. The transition from the soft-ferromagnetic to the ferromagnetic phase occurs at lower temperatures and is discontinuous, yet it does not fall into the conventional first-order class. Instead, it is characterized by a diverging escape time from an ordered magnetization state.

cond-mat.stat-mech↗

arXiv2024

Complete aging in the noisy voter model enhances consensus formation

We investigate the effects of aging in the noisy voter model considering that the probability to change states decays algebraically with age $τ$, defined as the time elapsed since adopting the current state. We study the complete aging scenario, which incorporates aging to both mechanisms of interaction: herding and idiosyncratic behavior, and compare it with the partial aging case, where aging affects only the herding mechanism. Analytical mean-field equations are derived, finding excellent agreement with agent-based simulations on a complete graph. We observe that complete aging enhances consensus formation, shifting the critical point to higher values compared to the partial aging case. However, when the aging probability decays asymptotically to zero for large $τ$, a steady state is not always attained for complete aging.

physics.soc-ph↗

arXiv2023

Aging in some opinion formation models: a comparative study

Changes of mind can become less likely the longer an agent has adopted a given opinion state. This resilience or inertia to change has been called ``aging''. We perform a comparative study of the effects of aging on the critical behavior of two standard opinion models with pairwise interactions. One of them is the voter model, which is a two-state model with a dynamic that proceeds by simple social contagion, another is the so-called kinetic exchange model, which allows a third (neutral) state and the formed opinion depends on the previous opinions of both interacting agents. Furthermore, in the noisy version of both models, random opinion changes are also allowed, regardless of the interactions. Due to aging, the probability of change diminishes with the age, and to take this into account we consider algebraic and exponential kernels. We investigate the situation where aging acts only on pairwise interactions. Analytical predictions for the critical curves of the order parameters are obtained for the opinion dynamics on a complete graph, in good agreement with agent-based simulations. For both models considered, consensus is optimized by an intermediate value of the parameter that rules the rate of decrease of the aging factor.

physics.soc-ph↗