"Wild sphere" of correlations
Zel'tser A. S. , Filippov A. E.
The fine structure of the spatial dispersion of a two-point correlation function of the fluctuating field at the critical point was investigated. It was shown numerically that the formation of a "filamentary" large-scale spatial structure of this field results in the fact that the Fourier transform of the correlation function of the field is strongly irregular (fractal) at low momenta. It was determined that such a fine structure of the correlation function is the physical reason for the nonintegral (anomalous) dimension of the smooth correlation function which is described in the analytic theory by Fisher's critical exponent η.
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![](/ps/1218/article_18424_800_head.png "The fine structure of the spatial dispersion of a two-point correlation function of the fluctuating field at the critical point was investigated. It was shown numerically that the formation of a "filamentary" large-scale spatial structure of this field results in the fact that the Fourier transform of the correlation function of the field is strongly irregular (fractal) at low momenta. It was determined that such a fine structure of the correlation function is the physical reason for the nonintegral (anomalous) dimension of the smooth correlation function which is described in the analytic theory by Fisher's critical exponent <i>η.</i>")