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Correlations, Susceptibility, and the Fluctuation–Dissipation Theorem

  • Sergey G. AbaimovEmail author
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In the previous chapters, we were acquainted with three complex systems. For each system, our primary interest was to find its equation of state. This is quite reasonable because the equation of state provides us with the averaged system’s response to the change of external field parameters. For example, if we know the dependence of the equilibrium magnetization on temperature and magnetic field for the Ising model, this knowledge is generally sufficient for practical applications. The equation of state, which represents the equilibrium state averaged over the ensemble, does not take into account the possibility of system’s fluctuations in the vicinity of this equilibrium state. But generally, we can neglect fluctuations because large fluctuations are improbable.

However, the situation changes drastically in the proximity of the critical point. The fluctuations become so large that they begin to dominate the system’s behavior, disguising the details of microscopic interactions of the system’s degrees of freedom. The laws of the system’s behavior no longer depend on what particular system we consider and become similar (universal) for very different systems. It no longer matters whether we consider the Ising model, percolation, or damage—any of these systems in the vicinity of its critical point forgets its own (specific for this particular system) laws of behavior and begins to obey the universal power-law dependencies.

Keywords

Correlation Function Partition Function Correlation Length Ising Model Percolation Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Advanced Structures, Processes and Engineered Materials CenterSkolkovo Institute of Science and TechnologySkolkovoRussia

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