The Lattice Cutoff for λϕ⁴₄ and λϕ⁶₃
Brahm, David E.
Original · EN
We analyze the critical line of λϕ⁴₄ perturbatively in the bare coupling λ₀, by setting the daisy-improved renormalized mass to zero. By comparing to lattice data, we can then quantify the relation between the continuum cutoff and the lattice spacing; for the 4-dimensional hypercubic lattice we find (Λa)C₄ = 4.893. We perform a similar analysis for λϕ⁶₃, and find in 3 dimensions (Λa)C₃ = 4.67. We present two theoretical predictions for (Λa). For small λ₀, both the critical line and the renormalized mass near criticality are easily and accurately calculated from the lattice input parameters.
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