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Gaussian Free Field in the background of correlated random clusters, formed by metallic nanoparticles
The effect of metallic nano-particles (MNPs) on the electrostatic potential
of a disordered 2D dielectric media is considered. The disorder in the media is
assumed to be white-noise Coulomb impurities with normal distribution. To
realize the correlations between the MNPs we have used the Ising model with an
artificial temperature that controls the number of MNPs as well as their
correlations. In the limit, one retrieves the Gaussian free
field (GFF), and in the finite temperature the problem is equivalent to a GFF
in iso-potential islands. The problem is argued to be equivalent to a
scale-invariant random surface with some critical exponents which vary with
and correspondingly are correlation-dependent. Two type of observables have
been considered: local and global quantities. We have observed that the MNPs
soften the random potential and reduce its statistical fluctuations. This
softening is observed in the local as well as the geometrical quantities. The
correlation function of the electrostatic and its total variance are observed
to be logarithmic just like the GFF, i.e. the roughness exponent remains zero
for all temperatures, whereas the proportionality constants scale with .
The fractal dimension of iso-potential lines (), the exponent of the
distribution function of the gyration radius (), and the loop lengths
(), and also the exponent of the loop Green function change in
terms of in a power-law fashion, with some critical exponents reported
in the text. Importantly we have observed that
, in which is the spin
correlation length in the Ising model
- β¦