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Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
Yuan Huang1, Kun Chen, Youjin Deng
1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. huangy22@mail.ustc.edu.cn
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
Summary
Infinite families of 2D lattices allow finite-temperature phase transitions for the q-state Potts antiferromagnet at large q values. This is proven using Peierls argument and validated by numerical methods.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Graph Theory
Background:
- The behavior of magnetic systems like the Potts model is crucial for understanding phase transitions.
- Investigating phase transitions on various lattice structures reveals fundamental properties of matter.
Purpose of the Study:
- To demonstrate the existence of infinite two-dimensional lattices supporting finite-temperature phase transitions for the q-state Potts antiferromagnet at arbitrarily large q.
- To rigorously prove this unexpected finding and support it with numerical evidence.
Main Methods:
- Rigorous proof using a Peierls argument to quantify the entropic advantage of sublattice long-range order.
- Numerical validation through transfer matrix calculations, Monte Carlo simulations, and graph-theoretic methods.
Main Results:
- Infinite families of 2D lattices, including triangulations and quadrangulations, exhibit a finite-temperature phase transition for the q-state Potts antiferromagnet at large q.
- The Peierls argument confirms the entropic basis for this transition.
Conclusions:
- The study establishes that specific 2D lattice geometries enable phase transitions in the Potts antiferromagnet even for a large number of states.
- This finding challenges previous assumptions about the relationship between the number of states and the occurrence of phase transitions in such systems.
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