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Zero-temperature random-field Ising model on a bilayered Bethe lattice
Thomas P Handford1, Francisco J Pérez-Reche, Sergei N Taraskin
1Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
Summary
Investigating the random-field Ising model on a bilayered Bethe lattice reveals infinite avalanches. Paradoxically, weakening interlayer interactions can trigger a phase transition to discontinuous magnetization reversal.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Computational Physics
Background:
- The random-field Ising model is crucial for understanding magnetic materials and disordered systems.
- Infinite avalanches in such models are observed but their underlying mechanisms require detailed investigation.
- Bilayered structures introduce complex interactions that influence system behavior.
Purpose of the Study:
- To analytically solve the zero-temperature random-field Ising model for magnetization on a bilayered Bethe lattice.
- To establish the mechanisms behind infinite avalanches, particularly at low disorder levels.
- To investigate the impact of varying interlayer interaction strengths on these avalanches and phase transitions.
Main Methods:
- Analytical solution of the zero-temperature random-field Ising model.
- Calculation of magnetization as a function of external field.
- Direct Monte Carlo simulations of spin-flip dynamics to validate analytical results.
- Analysis of spin-field correlation length and its critical behavior.
Main Results:
- Mechanisms for infinite avalanches at low disorder were established.
- The influence of interlayer interaction strength on infinite avalanches was quantified.
- A paradoxical phase transition was observed: reducing interlayer bond strength can shift from continuous to discontinuous magnetization reversal, driven by infinite avalanches.
Conclusions:
- The study provides an analytical framework for understanding magnetization reversal and avalanches in bilayered systems.
- The findings highlight a counterintuitive relationship between interlayer coupling and phase transitions in disordered magnetic systems.
- Monte Carlo simulations confirm the analytical predictions, reinforcing the validity of the proposed avalanche mechanisms.
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