A Lower Bound on $T_{SR}/{m_{\rm H}}$ in the O(4) Model on Anisotropic Lattices

Details A Lower Bound on $T_{SR}/{m_{\rm H}}$ in the O(4) Model on Anisotropic Lattices A Lower Bound on $T_{SR}/{m_{\rm H}}$ in the O(4) Model on Anisotropic Lattices

1992-07-31

arxiv.org/abs/hep-lat/9207033v1

Phys.Lett. B294 (1992) 84-90

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages with 4 ps figures included. LaTeX file. BI-TP 92/27, FSU-SCRI-92-101, HLRZ-92-40, TIFR/TH/92-42

Scientific paper

10.1016/0370-2693(92)91644-O

Results of an investigation of the $O(4)$ spin model at finite temperature using anisotropic lattices are presented. In both the large $N$ approximation and numerical simulations using the Wolff cluster algorithm we find that the ratio of the symmetry restoration temperature $T_{\rm SR}$ to the Higgs mass $m_{\rm H}$ is independent of the anisotropy $\xi$. From the numerical simulations we obtain a lower bound of $T_{\rm SR} / m_{\rm H} \simeq 0.58 \pm 0.02$ at a value for the Higgs mass $m_{\rm H}a_s \simeq 0.5$, which is lowered further by about $10\%$ at $m_{\rm H}a_s \simeq 1$. Requiring certain timelike correlation functions to coincide with their spacelike counterparts, quantum and scaling corrections to the anisotropy are determined and are found to be small, i.e., the anisotropy is found to be close to the ratio of spacelike and timelike lattice spacings.

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