Size Scaling Exponent Research Articles

Remanent magnetization of a simple ferromagnet.

We have measured the remanent magnetization of single-crystal EuS from ${10}^{\mathrm{\ensuremath{-}}4}$ to ${10}^{4}$ sec after removing an applied field. Using a recent model for magnon relaxation on finite domains, the data yield size-scaling exponents of \ensuremath{\theta}=-0.10\ifmmode\pm\else\textpm\fi{}0.02 and \ensuremath{\zeta}=0.669\ifmmode\pm\else\textpm\fi{}0.004, in excellent agreement with exact theoretical predictions. As a function of temperature, the remanent magnetization is a maximum above the Curie transition, and for some thermal histories, becomes negative in the ferromagnetic regime. The behavior is consistent with a percolation backbone that is negatively coupled to the finite domains.

Studies on universality in two dimensional fractal media

Elasticity and electricity (dielectricity and conductivity) equations in two-dimensional inhomogeneous media are compared. In the case of perpendicular vibration, the elasticity equation can be transformed into the exact formulation of the dielectricity one; therefore, electricity and elasticity belong to the same universal class and have the same size scaling exponent in the fractal system.

Studies on the scaling exponents of conductivity for Sierpinski carpets

The size scaling exponents alpha of the DC conductivity of Sierpinski carpets made of conductive paper are measured, and the possible relations between the exponent alpha and the fractal dimension df, the symmetry and the topology of carpets are studied. For some sequences of the carpets, the authors find that alpha can be expressed as the convenient power law alpha varies as (2-df)eta and the exponent eta is not sensitive to the geometry of the carpets and is almost constant (about 0.96) in some region beta (from 0.6 to 1.6), where beta is a control parameter used to describe other properties then fractal dimension, such as the symmetry of the sequences of carpets and is defined by the ratio of the void sections along the x direction to those along the y direction in the carpet. The relation between the spectral dimension ds and the geometry of the carpet is also discussed.

Studies of the spectral dimension for branched Koch curves

The scaling behaviour of Koch curves with a rather general branched structure is studied by means of the exact renormalisation method and the general formula of spectral dimension is obtained. It is proved that the spectral dimension is only dependent on the topology of the curve. The Einstein relation between the random walk dimension, fractal dimension and size-scaling exponent of DC conductivity is also checked.