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We study the effect of thermal fluctuations on the wetting phase transitionsof infinite order and of continuously varying order, recently discovered withina mean-field density-functional model for three-phase equilibria in systemswith short-range forces and a two-component order parameter. Using linearfunctional renormalization group (RG) calculations within a local interfaceHamiltonian approach, we show that the infinite-order transitions are robust.The exponential singularity (implying $2-\alpha_s = \infty$) of the surfacefree energy excess at infinite-order wetting as well as the precise algebraicdivergence (with $\beta_s = -1$) of the wetting layer thickness are notmodified as long as $\omega < 2$, with $\omega$ the dimensionless wettingparameter that measures the strength of thermal fluctuations. The interfacewidth diverges algebraically and universally (with $\nu_{\perp} = 1/2$). Incontrast, the non-universal critical wetting transitions of finite butcontinuously varying order are modified when thermal fluctuations are takeninto account, in line with predictions from earlier calculations on similarmodels displaying weak, intermediate and strong fluctuation regimes.

Renormalization group calculations for wetting transitions of infinite order and continuously varying order. I. Local interface Hamiltonian approach