Among physical phenomena, phase transitions are known to elude a simple physical description: they are in fact characterized by sudden change in macroscopic properties as the temperature is varied (e.g. in melting of ice or in the loss of magnetization of a magnet when heated). A new research work by Guido Giachetti, Nicolò Defenu, Stefano Ruffo, and Andrea Trombettoni has investigated the effect of long-range interactions on phase transition. The article, entitled "Berezinskii-Kosterlitz-Thouless Phase Transitions with Long-Range Couplings", has been just published in the scientific journal Physical Review Letters.
One way to understand usual phase transitions is that, although every component of the system such as the atoms in a crystalline lattice "sees" only neighboring ones, at the transition temperature they manage to communicate indirectly at long distance, ordering the system. By contrast, in long-range interacting systems, each component can directly influence far away ones, thus facilitating the phase transition. In their study, the paper's authors explored the effect of long-range interactions on the celebrated XY model in two dimensions. XY model can be used to describes magnetic as well as superfluid systems in terms of microscopical "compasses" on a plane. The phase transition associated with the model is a peculiar one: it can be understood by thinking that compasses organize themselves in large vortices, whose proliferation breaks the ordering.
The presence of a residual interaction between far-away pairs of points within each vortex is the reason why the understanding the long-range interacting version of XY model has eluded any effort so far. "In the new piece of research" Guido Giachetti says "we discovered that, in some cases, we have the appearance of a second transition temperature, of a completely new kind, under which long-range interaction destroys vortices. This result constitutes a further milestone in the understanding of long-range interacting systems, and could be important for experimental realizations in atomic and optical quantum systems".