1999
DOI: 10.1103/physreve.60.7558
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Test of renormalization predictions for universal finite-size scaling functions

Abstract: We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously found for short-range interactions, this leads to a singular expansion, where is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that can be varied continuously, allowing an accurate examination of the regio… Show more

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Cited by 24 publications
(50 citation statements)
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“…In particular, it can be mapped onto a one-dimesional lattice with z−2 SW interactions. This model is studied to determine whether the scaling for it is that of [25] or of another form predicted by Brézin and Zinn-Justin [26] and utilized to study Ising systems with long-range interactions [27][28][29][30].…”
Section: Model and Methodsmentioning
confidence: 99%
“…In particular, it can be mapped onto a one-dimesional lattice with z−2 SW interactions. This model is studied to determine whether the scaling for it is that of [25] or of another form predicted by Brézin and Zinn-Justin [26] and utilized to study Ising systems with long-range interactions [27][28][29][30].…”
Section: Model and Methodsmentioning
confidence: 99%
“…Remarkably, the most prominent deviations from linearity occur near s 2 2 h sr , while the´0 expansion predicts a square-root-like singularity at the opposite end of the intermediate range [16].…”
mentioning
confidence: 99%
“…[14,15]. In the intermediate regime, finally, Q has been calculated by means of a singular expansion in´0, up to second order in p´0 [16,17]. From the magnetic susceptibility, which diverges as L g͞n at criticality, h can be extracted using the scaling law g ͑2 2 h͒n.…”
mentioning
confidence: 99%
“…These results were generalized to the O(n) vector ϕ 4 model by means of perturbation theory in combination with the renormalization group (RG) technique near the upper critical dimension [18,19,20,21,22,23] d = 2σ, lower critical dimension [24,25,26] d = σ, and the 1/n-expansion [27,28]. Computer simulations also contributed to the exploration of the critical properties of such systems [29,30,31,32,33,34,35].…”
Section: Basic Results In the Bulk Casementioning
confidence: 99%