Phase structure and critical behavior of lattice φ⁴ theory at different temperatures

The Variational-Cumulant Expansion method is applied to investigate the phase structure and the critical behavior of lattice φ⁴ theory at two different temperatures. The phase diagrams, the external current J as a function of the expectation value of the field operator 〈φ_L〉 are calculated to the third order analytically. The critical behaviors of the expectation value 〈φ_L〉, the renormalized mass m_R and m_R/〈φ_L〉 are given and compared with the mean-field scaling laws with logarithmic scaling corrections. It is shown that, at a fixed bare coupling, the broken phase at a lower temperature might be restored at a higher temperature and a bound on the Higgs-boson mass at definite temperature can exist.