Skip to main content

Nonlinear sigma models with compact hyperbolic target spaces

Author(s): Gubser, Steven S.; Saleem, Zain H; Schoenholz, Samuel S; Stoica, Bogdan; Stokes, James

To refer to this page use:
Abstract: We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1,2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Publication Date: Jun-2016
Electronic Publication Date: 23-Jun-2016
Citation: Gubser, Steven, Saleem, Zain H, Schoenholz, Samuel S, Stoica, Bogdan, Stokes, James. (2016). Nonlinear sigma models with compact hyperbolic target spaces. Journal of High Energy Physics, 2016 (6), 10.1007/JHEP06(2016)145
DOI: doi:10.1007/JHEP06(2016)145
EISSN: 1029-8479
Pages: 1-14
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.