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arXiv · 2512.16536

Critical coupling in $ϕ_2^4$ theory

Stephan Durr·Tolga S. H. Kiel
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Abstract

We consider $ϕ^4$ theory with $ϕ(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hatλ$ the (negative) critical bare mass $\hatμ_{0\mathrm{c}}^2(\hatλ)$ where the lattice-regularized system changes from the symmetric to the broken phase. Based on these data, the transition to infinite volume and a universal scheme with the renormalized parameter $\hatμ_\mathrm{c}^2(\hatλ)$ is made. Finally, $f_\mathrm{c}=\lim_{\hatλ\to0}\hatλ/\hatμ_\mathrm{c}^2(\hatλ)$ is determined, with a judicious choice of the parameterizations considered. Our final result reads $f_\mathrm{c}=11.1097(20)_\mathrm{stat}(09)_\mathrm{sys}=11.1097(22)_\mathrm{tot}$.

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Stephan Durr, Tolga S. H. Kiel. 2025-12-18. Critical coupling in $ϕ_2^4$ theory. https://arxiv.org/abs/2512.16536

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