Renormalization group by Information Theory methods

Abstract

Renormalization group (RG) is a mathematical technique that allows to investigate how a physical system, such as a paramagnet, changes as one changes the observation scale. Initially grown in the context of particle physics and later on in the physics of critical phenomena RG has found its route to applications with Kenneth Wilson (Nobel laureate 1982). Real space RG is typically limited by the proliferation of interaction couplings in the Potential energy of the system. What is usually done is to approximate the RG recursion equations by truncation and accurate results are obtainable at the high cost to follows RG flows of many interaction couplings. The goal of the thesis is to use Information Theory in order to ‘‘project’’ the renormalized potential in the same space of the original potential so that as much information as possible is retained rather than using truncation, which has no justification apart from being practical.

References

  • Maris, Humphrey J., and Leo P. Kadanoff. ‘‘Teaching the renormalization group.’’ American Journal of Physics 46.6 (1978): 652-657 and reference therein.
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LIPh
Laboratory of Interdisciplinary Physics

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