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Two-parameter scaling of correlation functions near continuous phase transitions.
Nils Hasselmann1, Andreas Sinner, Peter Kopietz
1Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
This study introduces a new scaling form for the order parameter correlation function near continuous phase transitions. This approach captures the full critical regime and the crossover from classical to critical behavior.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Continuous phase transitions are characterized by diverging correlation lengths.
- Existing scaling theories often simplify behavior in the critical regime.
Purpose of the Study:
- To introduce and analyze a two-parameter scaling form for the order parameter correlation function.
- To describe the entire critical regime, including the classical-to-critical crossover.
- To investigate the behavior within the Ising universality class.
Main Methods:
- Utilizing a two-parameter scaling form: G(k)=kc(-2)g(kxi,k/kc).
- Analyzing the role of the nonuniversal momentum scale kc.
- Employing the functional renormalization group for calculations.
Main Results:
- The proposed scaling form G(k)=kc(-2)g(kxi,k/kc) describes the complete critical regime.
- The correlation function captures the classical-to-critical crossover.
- One-parameter scaling is a limiting case (k/kc-->0).
- An approximate calculation of g(x,y) for the Ising universality class was performed.
Conclusions:
- The two-parameter scaling form provides a comprehensive description of critical phenomena.
- The functional renormalization group offers a viable method for calculating critical behavior.
- This work advances the understanding of order parameter correlations near phase transitions.
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