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arXiv · 2512.16536

Critical coupling in $\phi_2^4$ theory

Stephan Durr·Tolga S. H. Kiel
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Abstract

We consider $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\lambda}$ the (negative) critical bare mass $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ 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 $\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ is made. Finally, $f_\mathrm{c}=\lim_{\hat{\lambda}\to0}\hat{\lambda}/\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ 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 $\phi_2^4$ theory. https://arxiv.org/abs/2512.16536

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