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Universal magnetic fluctuations with a field-induced length scale.
B Portelli1, P C Holdsworth, M Sellitto
1Laboratoire de Physique, Ecole Normale Supérieure, 46 Allée d'Italie, F-69364 Lyon Cedex 07, France.
Summary
We analyzed order-parameter fluctuations in the 2D XY model, finding universal non-Gaussian distributions. A new function, a(h), can measure correlation length scales in complex systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Magnetism
Background:
- The two-dimensional XY model is crucial for understanding phase transitions.
- Order-parameter fluctuations near critical points exhibit complex behavior.
Purpose of the Study:
- To calculate the probability density function for order-parameter fluctuations.
- To introduce a method for measuring correlation length scales in complex systems.
Main Methods:
- Hartree approximation to treat nonlinear field energy contributions.
- Analytical derivation of correlation length (xi) dependence on magnetic field (h).
- Development of a finite-size scaling form for probability distributions.
Main Results:
- Identified universal non-Gaussian probability density functions.
- Derived an analytical expression for the correlation length xi(h).
- Proposed a function P(x) ~ [exp[x-exp(x)]]^(a(h)) approximating the distributions.
Conclusions:
- The derived function a(h) serves as an indirect measure of correlation length.
- This approach offers insights into complex systems beyond the XY model.
- Non-Gaussian distributions are a key feature of critical phenomena in this model.