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For theories that exhibit second order phase transition, we conjecture thatthe large-order asymptotic behavior of the strong-coupling ( High-Temperature)series expansion takes the form $\sigma^{n} n^{b}$ where $b$ is a universalparameter. The associated critical exponent is then given by $b+1$. The seriesitself can be approximated by the hypergeometric approximants $_{p}F_{p-1}$which can mimic the same large-order behavior of the given series. Near the tipof the branch cut, the hypergeometric function $_{p}F_{p-1}$ has a power-lawbehavior from which the critical exponent and critical coupling can beextracted. The conjecture has been tested in this work for the perturbationseries of the ground state energy of the Yang-Lee model as a strong-couplingform of the $\mathcal{PT}$-symmetric $i\phi^3$ theory and the High-Temperatureexpansion within the Ising model. From the known $b$ parameter for the Yang-Leemodel, we obtained the exact critical exponents which reflects the universalityof $b$. Very accurate prediction for $b$ has been obtained from the many ordersavailable for the High-Temperature series expansion of the Ising model which inturn predicts accurate critical exponent. Apart from critical exponents, thehypergeometric approximants for the Yang-Lee model show almost exactpredictions for the ground state energy from low orders of perturbation seriesas input.

Universal Large-order asymptotic behavior of the Strong-coupling and High-Temperature series expansions