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Published on: December 4, 2017
Self-similar variational perturbation theory for critical exponents
1Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany. klienert@physik.fu-berlin.de
Summary
We developed a faster method for calculating critical exponents in quantum field theory. This new approach provides accurate results, matching experimental data for superfluid helium.
Area of Science:
- Theoretical physics
- Quantum field theory
- Statistical mechanics
Background:
- Field theoretic variational perturbation theory is a method for approximating solutions in quantum field theory.
- Calculating critical exponents is crucial for understanding phase transitions.
- Previous methods required high-order expansions for accuracy.
Purpose of the Study:
- To accelerate the convergence of field theoretic variational perturbation theory.
- To obtain accurate analytic results for critical exponents of O(N)-symmetric phi(4) theory.
- To compare the results with experimental data and known theoretical limits.
Main Methods:
- Integration of self-similar approximation theory with field theoretic variational perturbation theory.
- Recalculation of critical exponents using three-loop perturbation expansions in 4-epsilon dimensions.
- Derivation of analytic expressions for the exponents.
Main Results:
- Achieved significantly accelerated convergence compared to standard methods.
- Obtained analytic results for critical exponents close to seventh-order approximations.
- Specific-heat exponent (alpha) shows good agreement with experimental values for superfluid helium (-0.0127).
- Analytic expressions correctly reproduce the known large-N behavior of exponents.
Conclusions:
- The combined theory offers a computationally efficient and accurate approach for critical phenomena.
- The method provides reliable predictions for critical exponents, validated by experimental data.
- This advancement has implications for understanding phase transitions in various physical systems.
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