Universal relations among critical amplitude. Calculations up to order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>for systems with continuous symmetry

C. Bervillier C. Bervillier
1976 Physical review. B, Solid state 147 citations

Abstract

A general derivation of the two-scale-factor universality is given using the renormalized ${\ensuremath{\varphi}}^{4}$ theory. As a consequence ten universal relations among critical amplitudes are obtained, any other universal relations being a combination of them. The situation is shown to be the same as for the scaling laws for critical exponents. The calculations up to order ${\ensuremath{\epsilon}}^{2}$ for systems with continuous symmetry are performed for some of these relations such as the specific-heat amplitudes ratio and ${R}_{\ensuremath{\xi}}^{+}$, which relates the amplitudes of the correlation length and of the specific heat, etc. Comparison with experiments and series results and, in particular, the discussion of the superfluid helium and RbMn${\mathrm{F}}_{3}$ cases, are repeated with our improved numerical results.

Keywords

AmplitudePhysicsUniversality (dynamical systems)ScalingOrder (exchange)Critical exponentScaling lawSuperfluidityMathematical physicsThermodynamicsQuantum mechanicsPhase transitionMathematicsGeometry

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Publication Info

Year
1976
Type
article
Volume
14
Issue
11
Pages
4964-4975
Citations
147
Access
Closed

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C. Bervillier (1976). Universal relations among critical amplitude. Calculations up to order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>for systems with continuous symmetry. Physical review. B, Solid state , 14 (11) , 4964-4975. https://doi.org/10.1103/physrevb.14.4964

Identifiers

DOI
10.1103/physrevb.14.4964