On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes

Abstract

We recently determined the exact fixed point equations and the spaces of solutions of the two-dimensional $R{P}^{N-1}$ and $C{P}^{N-1}$ models using scale invariant scattering theory. Here we discuss subtleties hidden in some solutions and related to the difference between ferromagnetic and antiferromagnetic interaction.

References in corpus (30)

• Loop models with crossings
• New Universality Classes for Two-Dimensional $\sigma$-Models
• O(N) and RP^{N-1} Models in Two Dimensions
• Three-dimensional antiferromagnetic CP(N-1) models
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• Classifying Potts critical lines
• On the question of universality in $\RPn$ and $\On$ Lattice Sigma Models
• Exact results for quenched bond randomness at criticality
• The nature of the continuum limit in the 2D $R{P}^2$ gauge model
• Possible Failure of Asymptotic Freedom in Two-Dimensional $R{P}^2$ and $R{P}^3$ $\sigma$-Models
• Phase Transitions In Two Planar Lattice Models And Topological Defects: A Monte Carlo Study
• Evidence for a topological transition in nematic-to-isotropic phase transition in two dimensions
• On superuniversality in the $q$-state Potts model with quenched disorder
• Numerical study of the enlarged O(5) symmetry of the 3-D antiferromagnetic RP2 spin model
• Critical points of coupled vector-Ising systems. Exact results
• Absence of nematic quasi-long-range order in two-dimensional liquid crystals with three director components
• Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS Model
• Exact results for the $O(N)$ model with quenched disorder
• Critical lines in the pure and disordered $O(N)$ model
• Particles, conformal invariance and criticality in pure and disordered systems
• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• On the phase diagram of the random bond $q$-state Potts model
• Two phase transitions in the two-dimensional nematic 3-vector model with no quasi long-range order: Monte Carlo simulation of the density of states
• Critical points in the $R{P}^{N-1}$ model
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Sine-Gordon description of the scaling three-state Potts antiferromagnet on the square lattice
• 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
• Field theory of scaling lattice models. The Potts antiferromagnet
• Critical points in coupled Potts models and correlated percolation

Cited by in corpus (2)

• Nonuniversality in random criticality
• Exact results for spin glass criticality