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

TL;DR

This paper investigates how thermal fluctuations influence wetting phase transitions of infinite order and varying order, confirming the robustness of infinite-order transitions while showing modifications in finite, varying order transitions using renormalization group methods.

Contribution

It applies linear functional renormalization group calculations to analyze the stability of infinite-order wetting transitions under thermal fluctuations within a local interface Hamiltonian framework.

Findings

Infinite-order wetting transitions are robust against thermal fluctuations.

Surface free energy singularity remains unchanged for fluctuations with  < 2.

Wetting layer thickness diverges algebraically with  = -1.

Abstract

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group (RG) calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying $2-\alpha_s = \infty$) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with $\beta_s = -1$) of the wetting layer thickness are not modified as long as $\omega < 2$, with $\omega$ the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with $\nu_{\perp} = 1/2$). In contrast, the non-universal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate and strong fluctuation regimes.