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Surface critical behavior of random systems: ordinary transition
Z E Usatenko1, M A Shpot, C K Hu
1Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, Lviv, 79011, Ukraine. pylyp@icmp.lviv.ua
Summary
This study investigates surface critical exponents in disordered Ising-like systems using field theory. Results reveal new exponents characterizing critical behavior in semi-infinite systems with quenched disorder.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Disordered Systems
Background:
- Understanding critical phenomena in systems with quenched disorder is crucial.
- Surface critical behavior differs from bulk behavior and requires specific theoretical treatment.
Purpose of the Study:
- To calculate surface critical exponents for the ordinary transition in semi-infinite, quenched dilute Ising-like systems.
- To extend existing theoretical calculations to higher orders and different dimensions.
Main Methods:
- Field theoretic approach applied directly in d=3 dimensions up to two-loop approximation.
- Calculations performed in d=4-epsilon dimensions, extending previous work.
- Numerical estimates obtained using Padé approximants for perturbation theory expansions.
Main Results:
- Surface critical exponents for the ordinary transition were calculated.
- Results in d=4-epsilon dimensions were extended to the next-to-leading order.
- New surface critical exponents characterizing the system's behavior were identified.
Conclusions:
- The critical behavior of semi-infinite systems with quenched bulk disorder is governed by a distinct set of surface critical exponents.
- The field theoretic approach provides a robust framework for studying such complex systems.
- Further theoretical and numerical investigations can refine these findings.