Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$

Abstract

We study the $O(N)$-invariant ${\varphi }^4$ model on the simple cubic lattice by using Monte Carlo simulations. By using a finite size scaling analysis, we obtain accurate estimates for the critical exponents $\nu$ and $\eta$ for $N=4$, $5$, $6$, $8$, $10$, and $12$. We study the model for each $N$ for at least three different values of the parameter $\lambda$ to control leading corrections to scaling. We compare our results with those obtained by other theoretical methods.

arXiv comment43 pages, 13 figures, 3 python scripts in the uploded source, text extended, references added, eq. (12) corrected

References in corpus (33)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• The nonperturbative functional renormalization group and its applications
• Precision Islands in the Ising and $O(N)$ Models
• Quantum Field Theory in the Large N Limit: a review
• Critical behavior of the three-dimensional XY universality class
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Ising Universality in Three Dimensions: A Monte Carlo Study
• The critical exponents of the superfluid transition in He4
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• Bootstrapping the O(N) Archipelago
• Carving out OPE space and precise $O(2)$ model critical exponents
• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• 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}
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Numbers and Functions in Quantum Field Theory
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Monte Carlo study of an improved clock model in three dimensions
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
• Surface and bulk transitions in three-dimensional O(n) models
• The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
• The O(n) loop model on a three-dimensional lattice

Cited by in corpus (16)

• The critical O(N) CFT: Methods and conformal data
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Cubic fixed point in three dimensions: Monte Carlo simulations of the ${\varphi }^4$ model on the lattice
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• The regulator dependence in the functional renormalization group: a quantitative explanation
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Scaling functions of the three-dimensional $Z(2)$, $O(2)$ and $O(4)$ models and their finite size dependence in an external field
• The ordinary surface universality class of the three-dimensional O($N$) model
• Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O($N$)${}^{\ast }$ and Ising${}^{\ast }$ continuous transitions
• Conformal invariance constraints in the $O(N)$ models: a first study within the nonperturbative renormalization group
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
• Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
• Quenching through the QCD chiral phase transition
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model