# Critical Behaviour of Thermal Relaxation in Disordered Systems

Source: [Critical Behaviour of Thermal Relaxation in Disordered Systems](<https://www.sota2.com/research/paper/68fa1e417a2b558e29321379>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T14:34:19.135Z

Authors: C. D. Mukherjee, K. K. Bardhan

Published: 2003-03-17T15:12:22.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0303313>)

[PDF](<https://arxiv.org/pdf/cond-mat/0303313.pdf>)