Vortex Unbinding Transitions

Hrishikesh, G.P (2025) Vortex Unbinding Transitions. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of G.P Hrishikesh (20MS207)) 20MS207_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (11MB)

Abstract

Vortex unbinding transitions represent a fascinating class of phase transitions driven not by conventional symmetry breaking but by the topological rearrangement of defects. This work studies vortex unbinding transition in equilibrium and out-of-equilibrium cases. We explore vortex unbinding in granular systems through simple tabletop experiments. We study novel phenomena where the granular system spontaneously shows system-size circulation. We also attempt to construct a phenomenological model to capture the underlying physics. Vortex unbinding is also studied numerically in a coupled XY-Ising model. The Ising spins coupling adds inhomogeneity to the classical XY model. Although there is no one-to-one correspondence, the coupled XY-Ising model serves as an equilibrium analogue that captures key features of the experimental system. Chapter.I introduces the basic concepts used in statistical mechanics to characterize phase transition. Chapter.II describes the experiment, results obtained from experiments, and the proposed minimal models. Chapter.III introduces the role of vortices in the KT phase transition, introduces the Coupled XY-Ising model and the numerical study of the phase transitions using various order parameters of both Ising and KT classes.

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