  We study the phase transition in a class of fiber bundle models in which the
fiber strengths are distributed randomly within a finite interval and global
load sharing is assumed. The dynamics is expressed as recursion relations for
the redistribution of the applied stress and the evolution of the surviving
fraction of fibers. We show that an irreversible phase transition of
second-order occurs, from a phase of partial failure to a phase of total
failure, when the initial applied stress just exceeds a critical value. The
phase transition is characterised by static and dynamic critical properties. We
calculate exactly the critical value of the initial stress for three models of
this kind, each with a different distribution of fiber strengths. We derive the
exact expressions for the order parameter, the susceptibility to changes in the
initial applied sress and the critical relaxation of the surviving fraction of
fibers for all the three models. The static and dynamic critical exponents
obtained from these expressions are found to be universal.
