The stability of the O(N) invariant fixed point in three dimensions

Abstract

We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo simulations. It is well know that there is a critical value $2<N_c<4$ below which the O(N) fixed point is stable and above which the cubic fixed point becomes the stable one. While we cannot exclude that $N_c<3$, as recently claimed by Kleinert and collaborators, our analysis strongly suggests that $N_c$ coincides with 3.

latex file of 18 pages plus three ps figures

References in corpus (3)

• N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
• Universal Amplitude Ratios in the 3D Ising Model
• Five-loop \sqrtε-expansions for random Ising model and marginal spin dimensionality for cubic systems

Cited by in corpus (32)

• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Carving out OPE space and precise $O(2)$ model critical exponents
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• RG Flows and Bifurcations
• Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy
• Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ${\epsilon }^{1/2}$-Expansion
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ${\varphi }^4$ model
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• Multicritical behavior in models with two competing order parameters
• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• Stability of a cubic fixed point in three dimensions. Critical exponents for generic N
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice
• Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
• Magnetism in S=1/2 Double-Perovskites with Strong Spin-Orbit Interactions
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II
• Five-loop epsilon expansion for U(n)xU(m) models: finite-temperature phase transition in light QCD
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
• Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: the Case of Multiple-k Partial Order on the Pyrochlore Lattice
• Phase diagram of a system of hard cubes on the cubic lattice
• Renormalization group and nonlinear susceptibilities of cubic ferromagnets at criticality
• The stability of a cubic fixed point in three dimensions from the renormalization group
• Quantum criticality in a dissipative (2+1)-dimensional XY model of circulating currents in high-Tc cuprates
• Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO${}_4$
• Finite Size Scaling of the 2D Six-Clock model
• Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes
• Phases of the hard-plate lattice gas on a three-dimensional cubic lattice
• On the Stability of the O(N)-Invariant and the Cubic-Invariant 3-Dimensional $N$-Component Renormalization Group Fixed Points in the Hierarchical Approximation