Seminar

Real-world solids deviate from perfect crystalline structures due to topological defects called dislocations, which are characterized by Burgers' vectors and dislocation line vectors. These defects, forming loop-like structures due to continuity conditions, exhibit long-range interactions that complicate computational simulations. To address this challenge, researchers employ duality principles, connecting high and low-temperature properties of different statistical mechanical models. In three dimensions, the dual objects to dislocations are symmetric tensor loops with shortrange interactions, leading to first-order melting transitions. In contrast, non-symmetric tensor loop models, similar to those found in the dual model for vortices in the three-dimensional XY model, exhibit second-order phase transitions. This distinction raises questions about the relationship between loop characteristics and transition behavior, prompting investigations into the thermodynamic, non-equilibrium, and geometrical properties of non-symmetric loop models, particularly their percolation transitions.