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

Abstract

We study the $O(4)$-symmetric $ Φ^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $λ$. 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 $κ$ neighbouring the actually simulated ones. In the investigated vicinity of the critical point $κ_{c}$ finite volume effects affecting, e.g., the determination of the field expectation value $Σ$ and the mass $m_σ$ of the $σ$-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.