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Boundary-induced abrupt transition in the symmetric exclusion process
Apoorva Nagar1, Meesoon Ha, Hyunggyu Park
1School of Physics, Korea Institute for Advanced Study, Seoul, Korea.
Summary
We studied how boundaries affect particle movement in a system with competing local and nonlocal hopping. Open boundaries cause an abrupt phase transition from a dense to an empty state as nonlocal hopping increases.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Complex Systems
Background:
- The symmetric simple exclusion process (SSEP) is a fundamental model in statistical mechanics.
- Understanding phase transitions in systems with competing interactions and boundary conditions is crucial.
- Previous studies often focused on periodic boundary conditions, observing continuous transitions.
Purpose of the Study:
- To investigate the influence of open boundaries on the SSEP with competing nonlocal and local hopping.
- To identify and characterize the nature of phase transitions in this system.
- To elucidate the physical mechanisms driving the observed transitions.
Main Methods:
- Utilizing a cluster stability analysis to predict phase transition points.
- Performing numerical simulations to validate theoretical predictions.
- Comparing results from open boundary conditions with those from periodic boundaries.
Main Results:
- A first-order phase transition from a finite density phase to an empty road phase was observed with open boundaries.
- The nonlocal hopping rate was identified as the control parameter for this transition.
- The cluster analysis accurately predicted the transition location, aligning well with numerical data.
Conclusions:
- Open boundaries induce a discontinuous (first-order) phase transition in the SSEP with competing hopping.
- The observed discontinuity is attributed to the specific role of boundary conditions, contrasting with continuous transitions under periodic boundaries.
- Cluster stability analysis offers valuable physical insight into the transition mechanism.
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