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Generic power laws in higher-dimensional lattice models with multidirectional hopping.

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Conserved-mass transport on lattices with multidirectional hopping exhibits power-law correlations, even away from phase transitions. This algebraic decay arises from simultaneous mass movement in multiple directions, breaking detailed balance.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Conserved-mass transport models are crucial for understanding diffusion and phase transitions.
  • Detailed balance is a common assumption in physical processes, but its violation can lead to novel phenomena.
  • Multidirectional hopping offers a new mechanism for particle movement in lattice systems.

Purpose of the Study:

  • To investigate the correlation functions in conserved-mass transport processes on d-dimensional hypercubic lattices.
  • To determine the nature of correlations (power-law or short-ranged) arising from multidirectional hopping.
  • To explain the emergence of long-ranged correlations in systems like disordered hyperuniform matter.

Main Methods:

  • Utilizing hydrodynamic theory and exact microscopic theory.
  • Analyzing continuous-time Markov processes with multidirectional hopping.
  • Calculating steady-state static density-density and activity-density correlation functions.

Main Results:

  • Power-law correlations decaying as ~1/r^(d+2) are exhibited for generic parameter values in dimensions d>1.
  • The strength of these correlations is determined by diffusion coefficients and the Onsager matrix.
  • A restricted parameter regime shows short-ranged correlations.

Conclusions:

  • Multidirectional hopping in conserved-mass transport systems inherently leads to power-law correlations, breaking detailed balance.
  • The findings provide a theoretical explanation for long-ranged correlations observed in specific physical systems.
  • The study highlights the importance of considering non-detailed balance dynamics in statistical physics.