Vortex confinement transitions in the modified Goldstone model

Michikazu Kobayashi, Gergely Fejős, Chandrasekhar Chatterjee, Muneto Nitta

Research output: Contribution to journalArticlepeer-review


The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, or the O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of the model. Then, we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that field dependence of the wavefunction renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only one, but at two endpoints in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Aug 29

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Vortex confinement transitions in the modified Goldstone model'. Together they form a unique fingerprint.

Cite this