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

TL;DR

This paper uses Monte Carlo simulations to accurately estimate critical exponents of three-dimensional $O(N)$-invariant $^4$ models for various $N$, enhancing understanding of their critical behavior.

Contribution

It provides precise critical exponent estimates for $N=4,5,6,8,10,12$ using finite size scaling, and compares results with other theoretical approaches.

Findings

Accurate estimates of $ u$ and $ta$ for multiple $N$ values.

Analysis of correction-to-scaling effects across different $mbda$ values.

Comparison with existing theoretical predictions.

Abstract

We study the $O(N)$-invariant $\phi^4$ 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.