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Criticality in one dimension with inverse square-law potentials
1Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|June 1, 2001
Summary
The study reveals a universal critical jump in ferromagnetic Ising and Potts chains, similar to superfluid density. This finding provides strong evidence for Kosterlitz-Thouless-like phase transitions.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
Background:
- Ferromagnetic Ising and Potts models are fundamental in statistical mechanics.
- Understanding phase transitions in low-dimensional systems is crucial.
Purpose of the Study:
- To investigate the critical behavior of ferromagnetic Ising and three-state Potts chains with inverse square interactions.
- To demonstrate a universal critical jump in the scaled order parameter.
- To provide evidence for Kosterlitz-Thouless-like phase transitions.
Main Methods:
- Utilizing renormalization-group arguments.
- Performing numerical simulations on systems up to 10^6 lattice sites.
Main Results:
- Observed a universal critical jump in the scaled order parameter for both models.
- Quantitative evidence supporting a Kosterlitz-Thouless-like phase transition was found.
- Results contrast with and provide stronger evidence than earlier work.
Conclusions:
- The scaled order parameter exhibits a universal critical jump, analogous to superfluid density.
- The phase transition in these models is confirmed to be Kosterlitz-Thouless-like.
- This study offers robust quantitative validation of theoretical predictions.