[en] Complete text of publication follows. Although magnetic hysteresis is usually modeled as a set of equilibrium curves with jumps at critical fields, jumps will always occur before the critical field is reached because of thermal fluctuations. The probability of a jump at a given field depends on the network of connections between stable states by way of saddle points. The most difficult part of modeling such connections is finding the saddle points. A new method finds all the saddle points using a special tool for finding roots of polynomial systems. All equilibrium states are found and classified as stable, saddle, or other, and a two-stage solver finds the downhill paths from each saddle point to the nearest minima. A master equation is solved to get the time dependence of the magnetic moment. This method is applied to a chain of magnetostatically interacting single-domain particles such as those in magnetotactic bacteria. If there are N particles in a chain, there are up to 2^N saddle points. The number of saddle points decreases until there are at most two for particles in contact with each other. In zero field, the relaxation mode for chains of 5 or more particles is a new mode that I call the two-domain fanning mode. This mode has only a limited domain of stability and is replaced by a symmetric fanning mode in larger fields. If the critical size for the transition to superparamagnetism is expressed as the cube root of the volume, it approaches about 10 nanometers as the number of particles increases, independent of the shapes of the particles.

[en] Complete text of publication follows. If thermal fluctuations are ignored, the theory for isolated single-domain particles predicts a very simple hysteresis loop involving jumps between two stable magnetization curves. The associated first-order reversal curve (FORC) function for randomly oriented single-domain particles has some distinctive features that are observed in real samples: a negative region near the H_u axis and a sharp ridge (theoretically infinite) on the H_c axis. However, in real samples there is generally a symmetric spreading about the H_c axis that is not predicted by the theory. This could be due to particle interactions or thermal fluctuations. A new theory is developed for the effect of thermal interactions in systems of randomly oriented single-domain particles. As the field approaches the critical field for instability, the probability of a jump increases because the energy barrier between states is decreasing. The main hysteresis loop shrinks and the simple two-curve hysteresis of a given particle is replaced by an area in which a first-order reversal curve passes through every point. All jumps are replaced by continuous transitions, the ridge becomes finite, and the symmetry of the FORC function is broken.