The first - theoretical - paper describes the theory of why weak, oscillating magnetic fields might have an effect on the freezing of water. In a nutshell, it might be that nanocrystals of the mineral magnetite are the ice nucleating sites.
2013c Kobayashi, A. & J.L. Kirschvink, A ferromagnetic model for the action of electric and magnetic fields in cryopreservation. Cryobiology 68(2) 163-165.
The next paper demonstrated experimentally that nanophase magnetite added to ultra pure water stops water from supercooling!
2016c. Kobayashi, A., Golash, H.N., and J.L. Kirschvink, A First Test of the Hypothesis of Biogenic Magnetite-Based Heterogeneous Ice-Crystal Nucleation in Cryopreservation. Cryobiology Vol. 72, 216-224. doi:10.1016/j.cryobiol.2016.04.003
Our new paper shows that weak, oscillating magnetic field prevents ice nucleation even in water spiked with magnetite! And, it works on celery and beef!
2018a. Atsuko Kobayashi, Masamoto Horikawa, Joseph L. Kirschvink, and Harry N. Golash, Magnetic control of heterogeneous ice nucleation with nanophase magnetite: Biophysical and agricultural implications. PNAS, Published on-line May 07, 2018.