Scaling analysis of the O(4)-symmetric $Φ^4$-theory in the broken phase

Details Scaling analysis of the O(4)-symmetric $Φ^4$-theory in the broken phase Scaling analysis of the O(4)-symmetric $Φ^4$-theory in the broken phase

1992-06-29

arxiv.org/abs/hep-lat/9206025v1

Nucl.Phys. B404 (1993) 517-555

Physics

High Energy Physics

High Energy Physics - Lattice

34 pages, 9 PS-figures

Scientific paper

10.1016/0550-3213(93)90489-C

We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by applying the reflection cluster algorithm. Employing the histogram method we analytically continue to a sequence of values of the hopping parameter $\kappa$ neighbouring the actually simulated ones. In the investigated vicinity of the critical point $\kappa_{c}$ finite volume effects affecting, e.g., the determination of the field expectation value $\Sigma$ and the mass $m_\sigma$ of the $\sigma$-particle are very well described by 1-loop renormalized perturbation theory. We carry out a detailed scaling analysis on a high level of precision. Finally we discuss the upper bound on the Higgs mass for both kinds of actions.

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