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Position space renormalization and the breakdown of hyperscaling

H. J. F. Knops

Annals of the Israel Physical SocietyJan 1, 19780 citations

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

Hassan Chamati, Daniel Dantchev

arXiv:cond-mat/0109055The European Physical Journal BMar 1, 20026 citations

Effects of long-range interaction on critical and multicritical behavior of compressible disordered systems

С. В. Белим

A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a . A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a . A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.

arXiv:cond-mat/0502173Journal of Experimental and Theoretical PhysicsMay 1, 20050 citations

Ferromagnetic Phase Transitions in Random Fields: The Breakdown of Scaling Laws

G. Grinstein

The scaling laws relating the critical exponents characterizing the ferromagnetic phase transition are shown to be modified in the presence of quenched random magnetic fields. The hyperscaling relation $d\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, for example, becomes $(d+{\ensuremath{\lambda}}_{u})\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, where the index ${\ensuremath{\lambda}}_{u}$ is negative and is related to the range of the ferromagnetic exchange interactions. This breakdown of hyperscaling results from a singular dependence of the thermodynamic functions on the scaling field associated with an irrelevant operator.The scaling laws relating the critical exponents characterizing the ferromagnetic phase transition are shown to be modified in the presence of quenched random magnetic fields. The hyperscaling relation $d\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, for example, becomes $(d+{\ensuremath{\lambda}}_{u})\ensuremath{\nu}=2\ensuremath{-}\ensuremath{\alpha}$, where the index ${\ensuremath{\lambda}}_{u}$ is negative and is related to the range of the ferromagnetic exchange interactions. This breakdown of hyperscaling results from a singular dependence of the thermodynamic functions on the scaling field associated with an irrelevant operator.

Physical Review LettersOct 4, 1976277 citations

Finite-Size Scaling, Hyperscaling and the Renormalization Group

David Jasnow

WORLD SCIENTIFIC eBooksJan 1, 19902 citations

Progress and Problems in Real-Space Renormalization

Theodore W. Burkhardt, J. M. J. van Leeuwen

Topics in current physicsJan 1, 198211 citations

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

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Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

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