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Two-dimensional Ising model on random lattices with constant coordination number
Manuel Schrauth1, Julian A J Richter1, Jefferson S E Portela1,2
1Institute of Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
Physical Review. E
|March 18, 2018
Summary
Disordered two-dimensional Ising models exhibit varying critical exponents, suggesting no universal behavior. Lattice planarity and connectivity are crucial for stable phase transitions against topological disorder.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Network science
Background:
- The two-dimensional Ising model is a fundamental model in statistical mechanics.
- Understanding phase transitions in disordered systems is a key challenge.
- Topological disorder, or variations in network connectivity, can significantly alter system behavior.
Purpose of the Study:
- To investigate the impact of quenched topological disorder on the critical behavior of the two-dimensional Ising model.
- To determine if universal critical exponents emerge in disordered lattices.
- To explore the role of lattice planarity and connectedness in phase transition stability.
Main Methods:
- Construction of random lattices with constant coordination number.
- Large-scale Monte Carlo simulations.
- Application of finite-size scaling relations to extract critical exponents.
Main Results:
- Observed disorder-dependent effective critical exponents.
- Found behavior analogous to diluted Ising models, indicating a lack of clear universality.
- Results suggest topological disorder affects critical exponents.
Conclusions:
- The phase transition in the two-dimensional Ising model is sensitive to quenched topological disorder.
- Lattice planarity and connectedness are critical factors influencing the stability of phase transitions.
- Universal behavior is not guaranteed in the presence of significant topological disorder.
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