Critical points of coupled vector-Ising systems. Exact results

Abstract

We show that scale invariant scattering theory allows to exactly determine the critical points of two-dimensional systems with coupled $O(N)$ and Ising order pameters. The results are obtained for $N$ continuous and include criticality of loop gas type. In particular, for $N=1$ we exhibit three critical lines intersecting at the Berezinskii-Kosterlitz-Thouless transition point of the Gaussian model and related to the $Z_4$ symmetry of the isotropic Ashkin-Teller model. For $N=2$ we classify the critical points that can arise in the XY-Ising model and provide exact answers about the critical exponents of the fully frustrated XY model.

arXiv comment8 pages, 4 figures, 1 table

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Cited by in corpus (12)

• Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
• Particles, conformal invariance and criticality in pure and disordered systems
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Critical points in the $R{P}^{N-1}$ model
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Critical points in the $C{P}^{N-1}$ model
• Critical points in coupled Potts models and correlated percolation
• Weak universality induced by $Q=\pm 2e$ charges at the deconfinement transition of a (2+1)-d $U(1)$ lattice gauge theory
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Nonuniversality in random criticality
• Exact results for spin glass criticality