Three-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-invariant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math> models at criticality for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>

Abstract

We study the $O(N)$-invariant ${\ensuremath{\phi}}^{4}$ 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 $\ensuremath{\nu}$ and $\ensuremath{\eta}$ 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 $\ensuremath{\lambda}$ to control leading corrections to scaling. We compare our results with those obtained by other theoretical methods.

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