Condensation transition in a conserved generalized interacting zero-range process

Abstract

A conserved generalized zero range process is considered in which two sites interact such that particles hop from the more populated site to the other with a probability $p$. The steady state particle distribution function $P(n)$ is obtained using both analytical and numerical methods. The system goes through several phases as $p$ is varied. In particular, a condensate phase appears for $p_l<p<p_c$, where the bounding values depend on the range of interaction, with $p_c<0.5$ in general. Analysis of $P(n)$ in the condensate phase using a known scaling form shows there is universal behaviour in the short range process while the infinite range process displays non-universality. In the non-condensate phase above $p_c$, two distinct regions are identified: $p_c<p\le 0.5$ and $p>0.5$; a scale emerges in the system in the latter and this feature is present for all ranges of interaction.

References in corpus (24)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Connectivity of Growing Random Networks
• Bose-Einstein condensation in complex networks
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Condensation in the zero range process: stationary and dynamical properties
• Criterion for phase separation in one-dimensional driven systems
• The Nature of the Condensate in Mass Transport Models
• Canonical Analysis of Condensation in Factorised Steady State
• Condensation in the Backgammon model
• Hysteretic clustering in granular gas
• Wealth Condensation in Pareto Macro-Economies
• Dynamics of the condensate in zero-range processes
• Interaction driven real-space condensation
• Zero range model of traffic flow
• Thermodynamic Limit for the Invariant Measures in Supercritical Zero Range Processes
• Conditional Distribution of Heavy Tailed Random Variables on Large Deviations of their Sum
• Condensation in stochastic mass transport models: beyond the zero-range process
• Modelling one-dimensional driven diffusive systems by the Zero-Range Process
• Condensation for a fixed number of independent random variables
• Mass condensation in one dimension with pair-factorized steady states
• Structure of the stationary state of the asymmetric target process
• Pair-factorized steady states on arbitrary graphs
• Opinion dynamics model with domain size dependent dynamics: novel features and new universality class