Screening of charged singularities of random fields

Details Screening of charged singularities of random fields Screening of charged singularities of random fields

2004-02-04

arxiv.org/abs/cond-mat/0402120v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, no figures. Minor revision of manuscript submitted to J. Phys. A, August 2003

Scientific paper

10.1088/0305-4470/37/26/012

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.

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