Critical Behaviour of Thermal Relaxation in Disordered Systems

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 ($I_b$) the resistance eventually reaches a steady value with a characteristic relaxation time ${\tau }_h$. The latter diverges with current $I$ as ${\tau }_h\sim {(1-I^2\mathrm{/}{I_b}^2)}^{-z}$. 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.