Critical Behavior of Disordered Systems with a Free Surface

TL;DR

This paper investigates how free boundaries influence the critical behavior of disordered systems, revealing that boundaries have a minor effect on bulk criticality in the ordinary transition but a more significant impact in the special transition, with calculated critical exponents compared to simulations.

Contribution

It provides a two-loop approximation analysis of surface critical phenomena in disordered systems with free boundaries, highlighting the boundary effects on bulk critical behavior and impurity influence.

Findings

Boundaries slightly affect bulk critical behavior in the ordinary transition.

Impurities have a negligible effect in the special transition.

Critical exponents are calculated and compared with computer simulations.

Abstract

The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk critical behavior is revealed. It is shown that the boundedness of the system slightly affects the regime of the bulk critical behavior in the case of the ordinary transition, whereas this effect is more noticeable in the case of the special transition. Surface critical phenomena are described for homogeneous and disordered systems, and the critical exponents are calculated in the two-loop approximation. It is shown that the effect of impurities is insignificant in the special phase transition, whereas it is more noticeable in the ordinary phase transition. The derived critical exponents are compared with the computer-simulation results.