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Related Experiment Video

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Finite-size scaling in anisotropic systems.

¹G. Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussée, 1784 Sofia, Bulgaria. tonchev@issp.bas.bg

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 16, 2007

Summary

We analyzed finite-size scaling in anisotropic O(N) systems. Critical exponents vary with direction, impacting systems with long-range interactions and specific geometries.

Area of Science:

Condensed matter physics
Statistical mechanics

Background:

Anisotropy in physical systems leads to direction-dependent critical exponents.
Systems with long-range interactions or near quantum critical points often exhibit anisotropy.
Geometric confinement and boundary conditions influence scaling behavior.

Purpose of the Study:

To present analytical results for finite-size scaling in anisotropic O(N) systems.
To investigate how direction-dependent critical exponents affect various physical systems.
To analyze the impact of specific geometric confinements on scaling properties.

Main Methods:

Analytical calculations in the N --> infinity limit for O(N) systems.
Utilizing the properties of generalized Mittag-Leffler functions to overcome computational challenges.

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Considering systems confined to a d-dimensional layer with specific boundary conditions.

Main Results:

Direction-dependent critical exponents (nu{ ||} and nu{ perpendicular}) were derived for anisotropic O(N) systems.
The study provides a framework for understanding finite-size scaling in systems with anisotropic long-range interactions.
Analytical results were obtained for systems with Lifshitz points and space-time anisotropy.

Conclusions:

Finite-size scaling in anisotropic systems is complex and direction-dependent.
The employed mathematical techniques are effective for analyzing such systems.
The findings are relevant for diverse physical systems exhibiting anisotropy and specific geometries.