Multichain models of conserved lattice gas

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• Conserved lattice-gas models in one dimension show simple absorbing state phase transitions (APTs).
• Models on a ladder typically fall under directed percolation (DP) universality.
• The role of additional stochasticity in particle transfer on APTs is a key question.

Purpose of the Study:

• To investigate the impact of restricted particle movement on absorbing state phase transitions in multichain lattice-gas models.
• To determine if additional stochasticity perturbs the system towards directed percolation universality.
• To analyze the critical behavior and exponents for different system configurations.

Main Methods:

• Introduction of a restricted conserved lattice-gas model on an M×L square lattice with periodic boundary conditions.
• Focus on particles with exactly one vacant neighbor, which move deterministically.
• Analytical treatment using the transfer-matrix method.

Main Results:

• For odd numbers of chains, APT occurs at ρ_{c}=1/2(1+1/M) with critical exponent β=1 in the thermodynamic limit.
• For even-chain systems, transitions occur at ρ_{c}=1/2.
• The critical exponent β varies for even chains: β=1, 2 for M=2, 4, and β=3 for M≥6, indicating unusual critical behavior.

Conclusions:

• The study confirms that restricted particle movement in conserved lattice-gas models on multichains leads to distinct absorbing state phase transitions.
• The critical behavior and exponents are shown to be dependent on the parity of the number of chains (M).
• The findings provide insights into universality classes and critical phenomena in complex lattice models.