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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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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.

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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.