Abstract
The critical behaviour of non-linear susceptibility of a two-component composite is studied in this paper. The first component of fraction p is non-linear and obeys a current - field (J - E) characteristic of the form 
while the second component of fraction q is linear with 
. Near the percolation threshold 
or 
, we examine the conductor - insulator (C - I) limit 
and superconductor - conductor (S - C) limit 
. For the C - I limit and 
, the effective linear and non-linear response functions behave as 
and 
, respectively. For the S - C limit and 
, 
and 
are found to diverge as 
and 
. Within the effective-medium approximation, the exponents are found to be s = t = 1 and 
, 
and 
. By using a connection between the non-linear response of the random non-linear composite problem and the resistance or conductance fluctuations of the corresponding random linear composite problem, the exponents 
and 
are found to be 
, 
, respectively, where t(s) is the conductivity exponent in a C - I(S - C) composite, d is the dimension of the composite and 
is the correlation-length exponent in d dimensions, 
and 
are given by 
, 
, where 
characterizes the scaling of the 
th cumulant of the global resistance (conductance) distribution due to local resistance (conductance) fluctuations in the corresponding linear C - I(S - C) composites, 
and 
. We prove that is a monotonically increasing function of 
while is a monotonically decreasing function of , which have the following special values: 
and 
; 
and 
; 
and 
. The critical behaviour of the non-linear susceptibility in a C - I composite is very different from that of the non-linear susceptibility in a S - C composite and some unexpected results of the critical behaviour of non-linear susceptibility in a C - I network are reported in this paper.
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