Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

TL;DR

This paper studies how surface phase transitions in three-dimensional disordered Ising systems change between special and ordinary types, revealing new critical exponents due to randomness.

Contribution

It provides the first calculation of surface crossover critical exponents in disordered Ising-like systems using a two-loop field theoretic approach in three dimensions.

Findings

Surface crossover exponent $oldsymbol{ ext{ extPhi}}$ differs from pure systems.

Surface critical exponents $oldsymbol{ extalpha_1}$ and $oldsymbol{ extalpha_{11}}$ are altered by disorder.

Disorder introduces a new set of critical exponents for the boundary behavior.

Abstract

We investigate the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent $\Phi$, the critical exponents of the layer, $\alpha_{1}$, and local specific heats, $\alpha_{11}$, by applying the field theoretic approach directly in three spatial dimensions ($d=3$) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Pad\'e and Pad\'e-Borel resummation techniques. We find that $\Phi$, $\alpha_{1}$, $\alpha_{11}$ obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results confirm that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.