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Multicritical absorbing phase transition in a class of exactly solvable models
Arijit Chatterjee1, P K Mohanty1
1CMP Division, Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhan Nagar, Kolkata 700064, India.
Physical Review. E
|January 14, 2017
Summary
This study investigates particle diffusion on a 1D lattice with a maximum separation constraint. Researchers found critical density thresholds and derived scaling exponents for particle clusters and activity.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Complex Systems
Background:
- Diffusion models on lattices are crucial for understanding transport phenomena.
- Hard-core particle systems exhibit complex behavior due to exclusion interactions.
- Absorbing state phase transitions are key features in many dynamic systems.
Purpose of the Study:
- To analyze the diffusion of hard-core particles on a 1D lattice with a separation constraint.
- To investigate the absorbing state phase transition and its critical properties.
- To determine the behavior of cluster densities and activity at the transition point.
Main Methods:
- Theoretical analysis using matrix product states to model the system's steady state.
- Derivation of analytical expressions for static exponents.
- Numerical simulations to study the time evolution of cluster densities.
Main Results:
- Identified a critical density threshold ρ_{c}=1/(n+1) for the absorbing state phase transition.
- Found that densities of 0-clusters (ϕ_{k}) and activity (ρ_{a}) vanish at the transition.
- Derived static exponents β_{k}=n-k and ν=1=η, and dynamic exponents α_{k}=(n-k)/2 and ν_{t}=2=z.
Conclusions:
- The system exhibits a well-defined absorbing phase transition governed by particle density.
- Scaling laws relating static and dynamic exponents (β=αν_{t} and ν_{t}=zν) are validated.
- The matrix product approach provides an effective framework for analyzing such constrained diffusion models.
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