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Winding number excitation detects phase transition in one-dimensional XY model with variable interaction range
1Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, Republic of Korea.
Summary
We numerically studied the one-dimensional XY model, finding that a nonlocal order parameter effectively detects transitions. This parameter, based on winding number distribution, reveals system characteristics beyond local magnetization.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Computational Physics
Background:
- The one-dimensional XY model is a fundamental system for studying critical phenomena.
- Understanding transitions in such models is crucial for diverse physical systems.
- Local order parameters may not fully capture complex behaviors in 1D systems.
Purpose of the Study:
- To numerically investigate the critical behavior of the 1D XY model with variable interaction range.
- To explore the effectiveness of both local and nonlocal order parameters in detecting phase transitions.
- To analyze topological excitations (winding numbers) in relation to system transitions.
Main Methods:
- Numerical simulations of the 1D XY model with varying interaction range (L) and system size (N).
- Calculation of the standard local order parameter (magnetization).
- Analysis of topological excitations using the winding number and its distribution width.
Main Results:
- The local magnetization order parameter correctly identifies the mean-field-type transition for any non-zero L/N.
- The system exhibits a mean-field transition despite its 1D structure, similar to globally coupled systems.
- A proposed nonlocal order parameter, based on winding number distribution width, clearly signals the system's transition nature.
Conclusions:
- The 1D XY model with variable interaction range displays a mean-field transition detectable by local order parameters.
- Topological excitations (winding numbers) provide insights into the system's behavior.
- A novel nonlocal order parameter based on winding number distribution width offers a sensitive probe for phase transitions in this model.
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