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Published on: November 16, 2013
Zeros of the partition function and pseudospinodals in long-range Ising models
Natali Gulbahce1, Harvey Gould, W Klein
1Department of Physics, Clark University, Worcester, Massachusetts 01610, USA.
Summary
Investigating Ising models, this study links partition function zeros to spinodal critical points in complex temperature/magnetic field space. These zeros approach real values as interaction range grows, clarifying phase transitions.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Ising models are fundamental for understanding magnetism and phase transitions.
- Spinodal points mark the limit of thermodynamic stability.
- Long-range interactions significantly alter critical phenomena.
Purpose of the Study:
- To investigate the relationship between partition function zeros and spinodal critical points.
- To explore this relationship in Ising models with long-range interactions.
- To understand the behavior of these zeros in complex parameter space.
Main Methods:
- Analysis of the partition function in four-dimensional complex temperature/magnetic field space.
- Theoretical investigation of Ising models with varying interaction ranges.
Main Results:
- A direct association is found between spinodal points and the zeros of the partition function.
- These zeros are located in four-dimensional complex temperature/magnetic field space.
- The zeros exhibit a tendency to approach the real temperature/magnetic field plane as interaction range increases.
Conclusions:
- The study provides a novel connection between microscopic properties (partition function zeros) and macroscopic instability points (spinodal).
- This finding offers a deeper theoretical understanding of phase transitions in systems with long-range interactions.
- The behavior of partition function zeros can serve as an indicator for critical phenomena in complex parameter spaces.
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