Critical Behaviour of Thermal Relaxation in Disordered Systems

TL;DR

This paper investigates the thermal relaxation behavior in disordered systems under Joule heating, revealing a divergence in relaxation time near a breakdown current and drawing parallels with critical phenomena.

Contribution

It introduces a model describing the divergence of relaxation time in disordered systems and compares it with thermodynamic critical phenomena, highlighting unusual scaling behavior.

Findings

Relaxation time diverges as current approaches breakdown current.

Exponent z shows large fluctuations, indicating complex scaling.

Comparison with thermodynamic critical phenomena enhances understanding.

Abstract

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 $\tau_h \sim {(1-I^2/ {I_b}^2)}^{-z}$. 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.