The static dielectric properties of Stockmayer fluids are investigated in the hyperspherical geometry, S(3). Different methods of obtaining the static dielectric constant ε(r) are compared. Tested methods include the evaluation of the Kirkwood factor, fluctuations of the total dipole moment, and a two-center potential correlation formula to obtain the dielectric constant through effective interactions. With no coupling to the "surrounding," the different methods give consistent estimates of the dielectric constant. Adding a coupling to the surrounding gives large size dependencies and the two-center potential correlation formula breaks down. For low dipole moments, there is a good agreement in the dielectric constant with previous studies.
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