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Refined Universality for Critical KCM: Upper Bounds.

Ivailo Hartarsky1

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This study classifies critical kinetically constrained models (KCM) into seven categories, refining previous classifications. It determines the infection time logarithm for all critical KCM, completing a universality program.

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Area of Science:

  • Statistical physics
  • Probability theory
  • Dynamical systems

Background:

  • Kinetically constrained models (KCM) are interacting particle systems linked to bootstrap percolation.
  • Critical KCM are extensively studied, with previous work determining infection times up to logarithmic corrections.

Purpose of the Study:

  • To determine the logarithm of the infection time for all critical KCM up to a constant factor.
  • To classify critical KCM into distinct categories based on their behavior.
  • To complete the universality program for equilibrium critical KCM.

Main Methods:

  • Analysis of interacting particle systems in two dimensions.
  • Leveraging techniques from the study of monotone cellular automata and bootstrap percolation.
  • Development of sophisticated and robust mathematical techniques for relaxation mechanisms.

Main Results:

  • Critical KCM are classified into seven categories, refining existing classifications.
  • The logarithm of the infection time is determined up to a constant factor for all critical KCM.
  • Upper bounds for five novel categories of critical KCM are established.

Conclusions:

  • The classification of critical KCM into seven categories provides a more precise understanding of their behavior.
  • The established bounds complete the universality program for equilibrium critical KCM.
  • The study introduces new methodologies for analyzing relaxation mechanisms in these systems.