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.

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