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Phase transitions in an Ising model on a Euclidean network.
Arnab Chatterjee1, Parongama Sen
1Theoretical Condensed Matter Physics Division and Centre for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India. arnab.chatterjee@saha.ac.in
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
Summary
This study explores the Ising model on a 1D network with long-range bonds. A finite temperature phase transition occurs, with critical exponents depending on bond probability for 0 <= delta < 2.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Network Science
Background:
- The Ising model is a fundamental tool for studying magnetism and phase transitions.
- One-dimensional systems often exhibit unique critical behaviors compared to higher dimensions.
- Introducing long-range interactions can significantly alter system properties.
Purpose of the Study:
- Investigate the critical behavior of the Ising model on a one-dimensional network with power-law distributed long-range bonds.
- Determine the range of the parameter delta (0 <= delta < 2) for which a finite temperature phase transition exists.
- Analyze how the critical exponents change with delta and compare with theoretical predictions.
Main Methods:
- Utilizing numerical simulations to study the Ising model on a one-dimensional lattice.
- Implementing finite-size scaling analysis to extract critical exponents.
- Varying the parameter delta, which governs the probability distribution of long-range bonds.
Main Results:
- A finite temperature phase transition was observed across the entire range of delta (0 <= delta < 2).
- For 0 <= delta < 1, finite-size scaling behavior aligns with mean-field exponents.
- For 1 <= delta <= 2, the critical exponents were found to be dependent on delta.
Conclusions:
- The presence of long-range bonds in a one-dimensional network leads to a finite temperature phase transition.
- The critical behavior transitions from mean-field-like to delta-dependent as the range of interactions increases.
- These findings offer insights into the impact of network topology on magnetic phase transitions.
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