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Volumn 81, Issue 6, 2010, Pages

Numerical studies of a one-dimensional three-spin spin-glass model with long-range interactions

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EID: 77954829972     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.81.064415     Document Type: Article
Times cited : (41)

References (42)
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    • The model studied in Ref. has R=0.88;
    • The model studied in Ref. has R = 0.88
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    • For a discussion of how finite-size scaling is modified in the region of mean-field exponents, see, for example, Refs.
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    • One can alternatively reexpress the FSS results in Eqs. in the following way. A thermodynamic quantity X has the finite-size scaling form X = L yx x [ L yT (T- tc ) , L yH h ], where yT =1/ν and yH = (d+2-η ) /2 are the thermal and magnetic exponents. The connection between LR and SR exponents is obtained by writing this in terms of the total number of spins N and equating the exponents, i.e., yT,LR = yT,SR / deff , yH,LR = yH,SR / deff , yX,LR = yX,SR / deff. In the same way, the analogous result for the correction to scaling exponent ω is ωLR = ωSR / deff. The relation involving yX does not apply for the correlation length since it refers to a linear dimension, rather than a volume, and so there is no factor of deff, see Eq. .
    • One can alternatively reexpress the FSS results in Eqs. in the following way. A thermodynamic quantity X has the finite-size scaling form X = L y X X [L y T (T - t c), L y H h], where y T = 1 / ν and y H = (d + 2 - η) / 2 are the thermal and magnetic exponents. The connection between LR and SR exponents is obtained by writing this in terms of the total number of spins N and equating the exponents, i.e., y T, LR = y T, SR / d eff, y H, LR = y H, SR / d eff, y X, LR = y X, SR / d eff. In the same way, the analogous result for the correction to scaling exponent ω is ω LR = ω SR / d eff. The relation involving y X does not apply for the correlation length since it refers to a linear dimension, rather than a volume, and so there is no factor of d eff, see Eq.
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    • This expression vanishes for σ= σc =2/3 as expected. Furthermore, using the connection between σ and the effective dimension of a short-range model in Eq. , we have ω= ωSR /d with ωSR = (d-6 ) /2, as expected at the trivial Gaussian fixed point in a cubic field theory (Ref.).
    • This expression vanishes for σ = σ c = 2 / 3 as expected. Furthermore, using the connection between σ and the effective dimension of a short-range model in Eq., we have ω = ω SR / d with ω SR = (d - 6) / 2, as expected at the trivial Gaussian fixed point in a cubic field theory (Ref.).
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