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Finite-size Nagle-Kardar model: Casimir force
Daniel Dantchev1,2,3, Nicholay Tonchev4, Joseph Rudnick2
1Bulgarian Academy of Sciences, Institute of Mechanics, Academic Georgy Bonchev St. Building 4, 1113 Sofia, Bulgaria.
Physical Review. E
|February 7, 2025
Summary
We derived exact results for the critical Casimir force in the Nagle-Kardar model. Unexpectedly, the force is repulsive near critical and tricritical points, violating the boundary condition rule.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Nagle-Kardar model describes a 1D Ising chain with competing interactions.
- Critical Casimir force (CCF) behavior is typically linked to boundary conditions.
Purpose of the Study:
- Derive exact results for CCF in the Nagle-Kardar model with periodic boundary conditions (PBCs).
- Investigate the influence of competing ferromagnetic and antiferromagnetic interactions on CCF.
Main Methods:
- Exact derivation of CCF for the Nagle-Kardar model.
- Analysis of the model in the thermodynamic limit with PBCs.
- Identification of critical and tricritical points.
Main Results:
- Identified a critical line and a tricritical point in the interaction parameter plane.
- CCF exhibits unusual repulsive behavior near critical and tricritical points with PBCs.
- Observed a violation of the standard boundary condition rule for CCF.
Conclusions:
- The CCF can be repulsive even with periodic boundary conditions, challenging established theories.
- The interplay of competing interactions and boundary conditions significantly alters CCF behavior.
- This study provides new insights into the universality classes of phase transitions.
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