Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
Martin Hasenbusch
TL;DR
This work extends the elimination of leading corrections to scaling to 3D O(3) and O(4) phi^4 models by identifying a finite coupling $\lambda^*$ where these corrections vanish, enabling highly precise estimates of universal exponents. Using Monte Carlo simulations combined with a finite size scaling framework built on RG-invariant, phenomenological couplings, the authors determine $\lambda^* \approx 4.4(7)$ for $N=3$ and $\lambda^* \approx 12.5(4.0)$ for $N=4$, and compute $\nu$ and $\eta$ at these points: for $N=3$, $\nu=0.710(2)$ and $\eta=0.0380(10)$; for $N=4$, $\nu=0.749(2)$ and $\eta=0.0365(10)$. The results align with field-theoretic analyses while offering improved precision by mitigating corrections to scaling, and they demonstrate the applicability of the lambda-star strategy to higher $N$. The approach supports more accurate comparisons with high-temperature series and continuum field theory, and it points to further gains from increased statistics and lattice sizes. Overall, the paper provides a robust methodology for reducing systematic errors in critical-exponent estimates for multi-component order parameters.
Abstract
We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size scaling method. We find that there exists a finite value of the coupling lambda^*, for both values of N, where leading corrections to scaling vanish. As a first application, we compute the critical exponents nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for N=4.