Dynamic surface critical behavior of systems with conserved bulk order parameter: Detailed RG analysis of the semi-infinite extensions of model B with and without nonconservative surface terms

TL;DR

This paper uses field-theoretic RG methods to analyze the dynamic surface critical behavior of semi-infinite systems described by model B, highlighting differences caused by nonconservative surface terms and providing explicit two-loop calculations.

Contribution

It provides a detailed RG analysis of semi-infinite model B with and without nonconservative surface terms, including explicit two-loop calculations and the characterization of distinct dynamic surface universality classes.

Findings

Models B_A and B_B exhibit distinct dynamic surface universality classes.

Differences in scaling functions for dynamic surface susceptibilities are identified.

One-loop RG calculations of susceptibilities are performed.

Abstract

The dynamic surface critical behavior of macroscopic systems whose dynamic bulk critical behavior is described by model $B$ is investigated. The semi-infinite extensions of bulk model $B$ introduced in a previous treatment [Phys. Rev. B 49, 2846 (1994)] and called models $B_A$ and $B_B$ are studied in detail by means of field-theoretic RG methods. The distinctive feature of these models is the presence or absence of relevant nonconservative surface terms. The earlier results on the structure of the required counterterms, the flow equations, and the representation of the surface critical exponents of dynamic quantities at the ordinary and special phase transitions in terms of static bulk and surface exponents are corroborated by means of an explicit two-loop calculation for $4-\epsilon$ dimensions. For parameter values corresponding to a given static surface universality class, models $B_A$ and $B_B$ represent distinct dynamic surface universality classes. Differences between these manifest themselves in the behavior of scaling functions for dynamic surface susceptibilities. RG-improved perturbation theory is used to compute some of these susceptibilities to one-loop order.