On the question of universality in $\RPn$ and $\On$ Lattice Sigma Models

Abstract

We argue that there is no essential violation of universality in the continuum limit of mixed $\RPn$ and $\On$ lattice sigma models in 2 dimensions, contrary to opposite claims in the literature.

16 pages (latex) + 3 figures (Postscript), uuencoded

References in corpus (4)

• Perfect lattice action for asymptotically free theories
• New Universality Classes for Two-Dimensional $\sigma$-Models
• Lattice Perturbation Theory for $O(N)$-Symmetric $\sigma$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory
• O(N) and RP^{N-1} Models in Two Dimensions

Cited by in corpus (22)

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• Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models
• Spin-stiffness and topological defects in two-dimensional frustrated spin systems
• The nature of the continuum limit in the 2D $R{P}^2$ gauge model
• The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
• Two-Dimensional Heisenberg Model with Nonlinear Interactions
• Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections
• Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
• Anti-Ferromagnetic Condensate in Yang-Mills Theory
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• First order transition induced by topological defects in the O(3) principal chiral model
• Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories
• Critical points in the $R{P}^{N-1}$ model
• Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Tensor Network Renormalization Study on the Crossover in Classical Heisenberg and $\mathrm{R}{\mathrm{P}}^2$ Models in Two Dimensions
• Critical points in the $C{P}^{N-1}$ model
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Topological defects and critical phenomena in two-dimensional frustrated helimagnets
• Gauged O(n) spin models in one dimension
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields