Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1996-01-29
Physics
High Energy Physics
High Energy Physics - Lattice
13 pages, 5 Postscript figures, uses epsf.sty
Scientific paper
10.1103/PhysRevB.55.8911
We compute the effective potential $V_{\rm eff}(\phi)$ for one-component real scalar field $\phi$ in three Euclidean dimensions (3D) in the case of spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising model in external field at temperatures approaching the phase transition from below. We study probability distributions of the order parameter on the lattices from $30^3$ to $74^3$, at $L/\xi \approx 10$. We find that, in close analogy with the symmetric case, $\phi^6$ plays an important role: $V_{\rm eff}(\phi)$ is very well approximated by the sum of $\phi^2$, $\phi^4$ and $\phi^6$ terms. An unexpected feature is the negative sign of the $\phi^4$ term. As close to the continuum limit as we can get ($\xi \approx 7.2$), we obtain $$ {\cal L}_{\rm eff} \approx {1 \over 2} \partial_\mu \phi \partial_\mu \phi + 1.7 (\phi^2 - \eta^2)^2 (\phi^2 + \eta^2). $$ We also compute several universal coupling constants and ratios, including the combination of critical amplitudes $C^- (f_1^-)^{-3} B^{-2}$.
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