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Error threshold in optimal coding, numerical criteria, and classes of universalities for complexity.

David B Saakian1

  • 1Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan. saakian@jerewan1.yerphi.am

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
Summary

Researchers calculated the free energy of the random energy model at a critical transition point. This point relates to error thresholds in optimal coding, revealing finite size corrections and defining complexity classes for various systems.

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Complexity Science

Background:

  • The study investigates the random energy model (REM) near the transition between ferromagnetic and spin glass phases.
  • This transition point is analogous to the decoding error threshold in optimal coding theory.

Purpose of the Study:

  • To calculate the free energy of the REM at the critical transition point.
  • To define and classify different universality classes based on complexity criteria.

Main Methods:

  • Calculation of free energy for the random energy model.
  • Analysis of finite size corrections at the transition point.
  • Development of complexity criteria and classification of systems.

Main Results:

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  • Finite size corrections to free energy are proportional to the square root of the number of degrees.
  • Magnetization response is maximal at half-values in the ferromagnetic phase.
  • A hierarchy of complexity classes is established, ranging from random graphs to living systems.

Conclusions:

  • The study provides a framework for understanding complexity across diverse scientific domains.
  • The concept of antiresonance is proposed as relevant for complex systems.
  • The findings link statistical mechanics models to information theory and biological systems.