P-adic numbers and replica symmetry breaking
Giorgio Parisi, Nicolas Sourlas
TL;DR
This paper introduces a p-adic number framework for replica symmetry breaking, showing ultrametricity as a natural outcome and highlighting the potential of p-adic Fourier transforms for simplifying properties.
Contribution
It presents a novel p-adic formulation of replica symmetry breaking, connecting ultrametricity with p-adic number properties and proposing p-adic Fourier transforms as a useful tool.
Findings
Ultrametricity arises naturally from p-adic properties.
Many properties of replica symmetry breaking can be derived simply.
p-adic Fourier transform is a promising analytical tool.
Abstract
The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be an promising tool.
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