Phase diagram, confining strings, and a new universality class in nematopolar matter

¹ Niels Bohr Institute, University of Copenhagen - Blegdamsvej 17, Copenhagen 2100, Denmark
² Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA
³ Center of Mathematical Sciences and Applications, Harvard University - Cambridge, MA 02138, USA

Received: 13 June 2025
Accepted: 10 November 2025

Abstract

We study a minimal model of a system with coexisting nematic and polar orientational orders, where one field tends to order and the other prefers isotropy. For strong coupling, the ordered field aligns the isotropic one, locking their orientations. The phase diagram reveals three distinct phases —nematopolar (aligned orders), nematic (independent orders), and isotropic (vanishing orders)— separated by continuous and discontinuous transitions, including a triple and a tricritical point. We find unique critical scaling for the nematopolar-nematic transition, distinct from standard nematic or polar universality classes. Additionally, in the locked nematopolar phase, we show nematic topological defect pairs are connected and confined by strings with constant tension. These strings arise from frustration in locking the orientational orders and can be interpreted as elongated cores of +1 polar topological defects. When a sufficiently strong background field couples to the polar order, all topological defects are expelled from the region. Analytical predictions are quantitatively confirmed by numerical simulations.