1. The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
2. MPI Research Inc., East Brunswick, New Jersey 08816, USA
3. Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02420, USA
4. School of Natural Sciences, University of California Merced, Merced, California 95344, USA
5. London Centre for Nanotechnology and Department of Physics and Astronomy, UCL, London WC1E 6BT, UK

Correspondence to: Correspondence and requests for materials should be addressed to T.F.R. (Email: tfr@uchicago.edu).

Most physical and biological systems are disordered, even though the majority of theoretical models treat disorder as a weak perturbation. One particularly simple system is a ferromagnet approaching its Curie temperature, T_C, where all of the spins associated with partially filled atomic shells acquire parallel orientation. With the addition of disorder by way of chemical substitution, the Curie point is suppressed, but no qualitatively new phenomena appear in bulk measurements as long as the disorder is truly random on the atomic scale and not so large as to eliminate ferromagnetism entirely¹. Here we report the discovery that a simply measured magnetic response is singular above the Curie temperature of a model, disordered magnet, and that the associated singularity grows to an anomalous divergence at T_C. The origin of the singular response is the random internal field induced by an external magnetic field transverse to the favoured direction for magnetization^{2, 3, 4}. The fact that ferromagnets can be studied easily and with high precision using bulk susceptibility and a large variety of imaging tools will not only advance fundamental studies of the random field problem, but also suggests a mechanism for tuning the strength of domain wall pinning, the key to applications.

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