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.

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

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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