Critical Behaviour of Thermal Relaxation in Disordered Systems

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At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of sufficiently large value is passed through the sample. If the current is less than a certain breakdown current (Ib) the resistance eventually reaches a steady value with a characteristic relaxation time τₕ. The latter diverges with current I as τₕ (1-I²/ Ib²)⁻ᶻ. The value of the exponent z displays large fluctuations leading to unusual scaling of the relaxation time. Comparisions with behaviour of thermodynamic dynamic critical phenomena are made.