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Related Experiment Video

Updated: Jul 10, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Renormalization of stochastic lattice models: basic formulation.

Christoph A Haselwandter1, Dimitri D Vvedensky

  • 1The Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
PubMed
Summary
This summary is machine-generated.

We present a multiscale analysis method for stochastic lattice models, deriving continuum equations from atomistic dynamics. This approach accurately describes systems across various length and time scales, validated with the Wolf-Villain model.

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Area of Science:

  • Statistical Physics
  • Computational Modeling
  • Multiscale Analysis

Background:

  • Stochastic lattice models are crucial for simulating complex systems.
  • Deriving continuum equations from atomistic rules is challenging.
  • Existing methods lack a unified approach for multiscale analysis.

Purpose of the Study:

  • To develop a general method for multiscale analysis of stochastic lattice models.
  • To systematically derive continuum equations from lattice model transition rules.
  • To establish a quantitative connection between atomistic dynamics and continuum descriptions.

Main Methods:

  • Lattice Langevin formulation for site fluctuations.
  • Regularization of transition rules to derive stochastic partial differential equations.
  • Renormalization-group (RG) trajectories for coarse-graining and scale bridging.

Main Results:

  • RG trajectories yield hierarchies of continuum equations across scales.
  • The method provides quantitative connections between different scales and atomistic dynamics.
  • Analysis of the 1D Wolf-Villain model shows excellent agreement with simulations.

Conclusions:

  • The developed method offers a systematic approach to derive multiscale continuum equations from lattice models.
  • This technique is applicable to a wide range of conservative lattice models and nonequilibrium systems.
  • The RG analysis reveals complex crossover sequences in stochastic differential equations.