A hierarchy of semidefinite programs provides rigorous bounds on spectral density functionals from Monte Carlo data subject to reflection positivity, converging to statistical error limits.
Monte Carlo determination of the critical coupling in $\phi^4_2$ theory
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abstract
We use lattice formulation of $\phi^4$ theory in order to investigate non--perturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant $g/\mu^2$ in the continuum, where $g$ is the {\em unrenormalised} coupling. Our final result is $g/\mu^2=11.15(6)(3)$.
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hep-lat 1years
2026 1verdicts
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Certified spectral functions from lattice Monte Carlo data
A hierarchy of semidefinite programs provides rigorous bounds on spectral density functionals from Monte Carlo data subject to reflection positivity, converging to statistical error limits.