Universal amplitude ratios in the 3D Ising model

Caselle, Michele; Hasenbusch, Martin

doi:10.1016/s0920-5632(97)00848-7

Cited by 12 publications

(14 citation statements)

References 25 publications

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“…It is important to stress that ξ 2 and ξ are not fully equivalent (cf. [3] ), even though their critical behaviours are the same up to a multiplicative factor. In particular, the ratio ξ/ξ 2 gives an idea of the density of the lowest states of the spectrum.…”

Section: Second Moment Correlation Lengthmentioning

confidence: 98%

“…Notice however that we used the simplest possible resummation technique, more sophisticated approaches like the double biased IDA of ref. [24] could give better results and could also give a way to estimate the systematic errors involved in the truncation and resummation of the series (for an attempt in this direction in the case of the 3d Ising model see for instance [3]) 5 . In the case of the susceptibility the discrepancy between the results from the series expansion and our Monte Carlo are larger and only the first value of beta agree within the errors.…”

Section: Magnetization and Susceptibilitymentioning

confidence: 99%

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Universal amplitude ratios in the 2D four-state Potts model

1999

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We present a Monte Carlo study of various universal amplitude ratios of the two dimensional q = 4 Potts model. We simulated the model close to criticality in both phases taking care to keep the systematic errors, due to finite size effects and logarithmic corrections in the scaling functions, under control. Our results are compatible with those recently obtained using the form-factors approach and with the existing low temperature series for the model.

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Section: Second Moment Correlation Lengthmentioning

confidence: 98%

Section: Magnetization and Susceptibilitymentioning

confidence: 99%

Universal amplitude ratios in the 2D four-state Potts model

1999

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“…All data with β ≥ β min are taken into account. Now we can compute the universal ratio by using the results (43,50):…”

Section: The Second Moment Correlation Length In the High Temperaturementioning

confidence: 99%

The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

Hasenbusch¹

2009

J. Stat. Mech.

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We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component φ 4 model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L 0 = 32 lattice spacings. In the short direction of the lattice free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U 4 , the second moment correlation length over the lattice size ξ 2nd /L, the ratio of the partition functions with antiperiodic and periodic boundary conditions Z a /Z p and the helicity modulus Υ clearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L 0 of the film. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L 0 and the transversal correlation length ξ T in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L 0 : [L 0,KT /ξ T ] * = 1.595 (7). This results can be compared with experimental results on thin films of 4 He near the λ-transition.

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“…Here instead we follow a strategy that had already been employed in ref. [24] where universal amplitude ratios for the three-dimensional Ising universality class had been computed. In order to eliminate the dependence of the result on the critical exponents, we consider ratios at a finite reduced temperature (24).…”

Section: Numerical Resultsmentioning

confidence: 99%

A Monte Carlo study of the three-dimensionalXYuniversality class: universal amplitude ratios

Hasenbusch¹

2008

J. Stat. Mech.

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We simulate lattice models in the three-dimensional XY universality class in the low and the high temperature phase. This allows us to compute a number of universal amplitude ratios with unprecedented precision: (10) and R − ξ = 0.850(5). These results can be compared with those obtained from other theoretical methods, such as field theoretic methods or the high temperature series expansion and also with experimental results for the λ-transition of 4 He. In addition to the XY model, we study the three-dimensional two-component φ 4 model on the simple cubic lattice. The parameter of the φ 4 model is chosen such that leading corrections to scaling are small.

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Universal amplitude ratios in the 3D Ising model

Cited by 12 publications

References 25 publications

Universal amplitude ratios in the 2D four-state Potts model

Universal amplitude ratios in the 2D four-state Potts model

The Kosterlitz–Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

A Monte Carlo study of the three-dimensionalXYuniversality class: universal amplitude ratios

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