InterJournal Complex Systems, 773
Status: Accepted
Manuscript Number: [773]
Submission Date: 2004
Universality classes of complexity
Author(s): David Saakian

Subject(s): CX.0

Category:

Abstract:

We calculate the free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases. At this point, equivalent to the decoding error threshold in optimal codes free energy has finite size corrections proportional to the square root of the number of degrees. The response of the magnetization to the external ferromagnetic is maximal at the values of magnetization equal to half. We give three criteria of complexity and define different universality classes. According to our classification at the lowest class of complexity are: Markov Models, maps, Hidden Markov Models. In a higher level are critical theories, percolation, self organized criticality (SOC). The next higher class involves: HOT design, error threshold in optimal coding, language and, maybe, financial market. Perhaps alive systems are also related with the last class.

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