Percolation and anisotropic conductivity, the Hall effect and thermopower in disordered systems

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Abstract
Second-order phase transitions are studied for anisotropic disordered systems composed of randomly distributed metal and non-metal regions, the former ones having tensor-type conductivity along the principal axes. Equations are derived for the effective Hall and Seebeck coefficients. It is shown that near the percolation threshold the decrease of the anisotropy of both the effective conductivity and Hall coefficient can be described by two new critical exponents that characterise the transition to the quasi-two-dimensional and the quasi-one-dimensional states. The anisotropy of the thermopower at close thermal conductivity values of the components is characterised by the same exponents that describe the electric conductivity, while at larger ratios of these values the thermopower anisotropy shows no decay at the non-metal side of the transition. The transition from the quasi-two-dimensional state to the two-dimensional one takes place at the two-dimensional threshold, while that from the quasi-one-dimensional state to the one-dimensional one occurs at the puncture threshold that depends on the size of the sample.