Modeling of phase transitions and patterns formation in ensembles of solitons
Peter Karpov (National University of Science and technology « MISiS », Moscow, Russia)
Vulnerability of broken symmetries of cooperative electronic states gives rise to topological defects like electronic vortices, walls, stripes. A typical quasi-one-dimensional architecture brings these objects to the microscopic scale giving rise to solitons as elementary particles taking from electrons their major roles as carriers of charge or spin. Because of the long-range ordering, the solitons experience unusual super-long-range forces leading to a sequence of phase transitions in their ensembles: the higher-temperature transition of the confinement and the lower one of aggregation into macroscopic walls.
In this talk I shall review the available analytical theory and present the recent results of an extensive numerical modeling for ensembles of both neutral and charged solitons in two- and three-dimensional systems. We suggest a specific Monte Carlo algorithm preserving the number of solitons, which substantially facilitates the calculations, allows to extend them to the three-dimensional case and to include the important long-range Coulomb interactions. The results confirm the first confinement transition, except for a very strong Coulomb repulsion, and demonstrate a pattern formation at the second transition of aggregation.
Reference: P. Karpov and S. Brazovskii, PRB 94, 125108 (2016).