A threshold induced phase transition in the kinetic exchange models

TL;DR

This paper investigates a kinetic exchange model with a phase transition driven by an energy threshold, revealing critical phenomena and different behaviors in mean field and lattice versions.

Contribution

It introduces a novel threshold-based kinetic exchange model exhibiting a phase transition with critical behavior, applicable in both mean field and lattice frameworks.

Findings

Existence of a critical energy threshold for phase transition.

Critical slowing down near the threshold.

Non-trivial critical exponents characterize the transition.

Abstract

We study an ideal-gas-like model where the particles exchange energy stochastically, through energy conserving scattering processes, which take place if and only if at least one of the two particles has energy below a certain energy threshold (interactions are initiated by such low energy particles). This model has an intriguing phase transition in the sense that there is a critical value of the energy threshold, below which the number of particles in the steady state goes to zero, and above which the average number of particles in the steady state is non-zero. This phase transition is associated with standard features like "critical slowing down" and non-trivial values of some critical exponents characterizing the variation of thermodynamic quantities near the threshold energy. The features are exhibited not only in the mean field version but also in the lattice versions.