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Updated: Jul 26, 2026
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Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Dynamical phase transition of a one-dimensional kinetic Ising model with boundaries
Mohammad Khorrami1, Amir Aghamohammadi
1Institute for Advanced Studies in Basic Sciences, P. O. Box 159, Zanjan 45195, Iran. mamwad@iasbs.ac.ir
Summary
This study examines the Glauber model on a 1D lattice, revealing a dynamical phase transition at all temperatures. This transition is governed by boundary spin flip rates, affecting relaxation time derivatives.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Glauber model is a fundamental tool for studying magnetic systems.
- Understanding large-time behavior and phase transitions in finite systems is crucial.
Purpose of the Study:
- To investigate the Glauber model on a one-dimensional lattice with boundaries.
- To analyze the large-time behavior of the one-point function.
- To identify and characterize dynamical phase transitions.
Main Methods:
- Analysis of the Glauber model on a 1D lattice with ferromagnetic and antiferromagnetic cases.
- Study of the large-time asymptotic behavior of the one-point function.
- Examination of the role of boundary conditions and spin flip rates.
Main Results:
- A dynamical phase transition occurs at any temperature in the considered system.
- The transition is controlled by the rate of spin flip at the boundaries.
- A discontinuous change in the derivative of the relaxation time towards the stationary state is observed.
Conclusions:
- The Glauber model on a 1D lattice with boundaries exhibits a temperature-independent dynamical phase transition.
- Boundary dynamics play a critical role in the system's relaxation behavior.
- This finding offers insights into non-equilibrium statistical mechanics.
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