Critical points in the $R{P}^{N-1}$ model

Abstract

The space of solutions of the exact renormalization group fixed point equations of the two-dimensional $R{P}^{N-1}$ model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of $N\ge 0$. Quasi-long-range order occurs only for $N=2$, and allows for several lines of fixed points meeting at the BKT transition point. A rich pattern of fixed points is present below $N^{\ast }=\mathrm{2.24421..}$, while only zero temperature criticality in the $O(N(N+1)/2-1)$ universality class can occur above this value. The interpretation of an extra solution at $N=3$ requires the identitication of a path to criticality specific to this value of $N$.

References in corpus (26)

• First-order transitions for n-vector models in two and more dimensions; rigorous proof
• Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
• Liquid crystals in two dimensions: First-order phase transitions and nonuniversal critical behavior
• Phase transition in a 2-dimensional Heisenberg model
• Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models
• New Universality Classes for Two-Dimensional $\sigma$-Models
• O(N) and RP^{N-1} Models in Two Dimensions
• 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
• Fields, particles and universality in two dimensions
• 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
• Exact results for quenched bond randomness at criticality
• Phase Transitions In Two Planar Lattice Models And Topological Defects: A Monte Carlo Study
• Liquid-gas and other unusual thermal phase transitions in some large-N magnets
• Evidence for a topological transition in nematic-to-isotropic phase transition in two dimensions
• Critical points of coupled vector-Ising systems. Exact results
• Numerical study of the enlarged O(5) symmetry of the 3-D antiferromagnetic RP2 spin model
• 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
• Critical lines in the pure and disordered $O(N)$ model
• Exact results for the $O(N)$ model with quenched disorder
• On the phase diagram of the random bond $q$-state Potts model
• Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories
• 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

Cited by in corpus (7)

• 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 coupled Potts models and correlated percolation
• Critical points in the $C{P}^{N-1}$ model
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes
• Nonuniversality in random criticality
• Exact results for spin glass criticality