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We study the phase transition in a class of fiber bundle models in which thefiber strengths are distributed randomly within a finite interval and globalload sharing is assumed. The dynamics is expressed as recursion relations forthe redistribution of the applied stress and the evolution of the survivingfraction of fibers. We show that an irreversible phase transition ofsecond-order occurs, from a phase of partial failure to a phase of totalfailure, when the initial applied stress just exceeds a critical value. Thephase transition is characterised by static and dynamic critical properties. Wecalculate exactly the critical value of the initial stress for three models ofthis kind, each with a different distribution of fiber strengths. We derive theexact expressions for the order parameter, the susceptibility to changes in theinitial applied sress and the critical relaxation of the surviving fraction offibers for all the three models. The static and dynamic critical exponentsobtained from these expressions are found to be universal.Comment: 15 pages (REVTeX4); 7 figures (eps); title and abstract modified;  paragraph of discussion added before section VI; three new references  included; to appear in Phys. Rev. E (2003

Phase transition in fiber bundle models with recursive dynamics