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Volumn 71, Issue 17, 2005, Pages

Finite-size scaling of the correlation length above the upper critical dimension in the five-dimensional Ising model

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EID: 33344476954     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.174438     Document Type: Article
Times cited : (53)

References (17)
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    • Erik Luijten (private communication) has pointed out that this prescription needs clarification in the presence of a magnetic field h. Standard FSS scaling functions then have a second argument, h Lσ, and the issue is what value to take for σ before the transformation L→l is made. If hyperscaling is satisfied then σ is equal to both yh = (d+2-η) 2 and Δν= (β+γ) ν. However, if hyperscaling is not satisfied, it is the latter expression that must be taken in order to get the correct behavior of bulk thermodynamic quantities. For d>4, we have (β+γ) ν=3 and, with the replacement L→l, the field enters the scaling functions in the combination h L3d4, in agreement with earlier work (see Refs.).
    • Erik Luijten (private communication) has pointed out that this prescription needs clarification in the presence of a magnetic field h. Standard FSS scaling functions then have a second argument, h Lσ, and the issue is what value to take for σ before the transformation L→l is made. If hyperscaling is satisfied then σ is equal to both yh = (d+2-η) 2 and Δν= (β+γ) ν. However, if hyperscaling is not satisfied, it is the latter expression that must be taken in order to get the correct behavior of bulk thermodynamic quantities. For d>4, we have (β+γ) ν=3 and, with the replacement L→l, the field enters the scaling functions in the combination h L3d4, in agreement with earlier work (see Refs.).
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