Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ξ</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="italic">L</mml:mi><mml:mi mathvariant="italic"/><mml:mi>≫</mml:mi><mml:mn>1</mml:mn></mml:math>

Caracciolo, Sergio; Edwards, Robert G.; Ferreira, Sabino José; Pelissetto, Andrea; Sokal, Alan D.

doi:10.1103/physrevlett.74.2969

Cited by 105 publications

(167 citation statements)

References 15 publications

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“…More precise estimates of ξ ⊥,∞ (β) can be obtained if we assume the validity of the JSLC theory and use the method of Ref. [40] to determine infinite-volume quantities.…”

Section: Resultsmentioning

confidence: 99%

Finite-Size Scaling in the Driven Lattice Gas

Caracciolo

Gambassi

Gubinelli

et al. 2004

Journal of Statistical Physics

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We present a Monte Carlo study of the high-temperature phase of the twodimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, verify that this definition has a good infinite-volume limit independent of the lattice geometry, and study its finite-size-scaling behavior. The results for the correlation length are in good agreement with the predictions based on the field theory proposed by Janssen, Schmittmann, Leung, and Cardy. The theoretical predictions for the susceptibility and the magnetization are also well verified. We show that the transverse Binder parameter vanishes at the critical point in all dimensions d ≥ 2 and discuss how such result should be expected in the theory of Janssen et al. in spite of the existence of a dangerously irrelevant operator. Our results confirm the Gaussian nature of the transverse excitations.

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“…More precise estimates of ξ ⊥,∞ (β) can be obtained if we assume the validity of the JSLC theory and use the method of Ref. [40] to determine infinite-volume quantities.…”

Section: Resultsmentioning

confidence: 99%

Finite-Size Scaling in the Driven Lattice Gas

Caracciolo

Gambassi

Gubinelli

et al. 2004

Journal of Statistical Physics

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“…Palassini and Caracciolo [3]. These works demonstrated the applicability to spin-glasses of our approach [4,5] to Finite Size Scaling (FSS) at the critical temperature, as well as that of Caracciolo and coworkers [6] for the paramagnetic state (see also [7,8]). …”

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confidence: 84%

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Campos¹,

Cotallo-Abán

Martı́n-Mayor

et al. 2006

Phys. Rev. Lett.

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It is shown, by means of Monte Carlo simulation and Finite Size Scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass orderings develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes possible to thermalize lattices of size L = 32, larger than in any previous spin glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allow us to consider scaling corrections. Palassini and Caracciolo [3]. These works demonstrated the applicability to spin-glasses of our approach [4,5] to Finite Size Scaling (FSS) at the critical temperature, as well as that of Caracciolo and coworkers [6] for the paramagnetic state (see also [7,8]).However, the situation is still confusing for Heisenberg spin glasses [9,10,11,12,13,14,15,16,17], which is the more experimentally interesting case (see e.g. [18,19]). Indeed, numerical studies are the only theoretical tool to achieve progress in three dimensions. Early simulations [9] could not reach low enough temperatures due to the dramatic dynamical arrest of the algorithms available at the time, and concluded that the critical temperature, T c , was strictly zero. Yet, recent studies at lower temperatures [16,17] found indirect indications of a spin glass transition for Heisenberg spin glasses. Matters are further complicated by the Villain et al. [12] suggestion of a low temperature chiral glass phase, with an Ising like ordering due to the handedness of the non-collinear spin structures (see definitions below). The simulations of Kawamura and coworkers [13,14] gave ample support to this spin-chirality decoupling scenario (i.e. T c = 0 for the spin glass, but T c > 0 for the chiral glass ordering).In order to clarify the situation for Heisenberg and XY spin glasses in D = 3, Young and Lee [15] have recently tried our FSS methods at T c [2,4]. Although parallel tempering only allowed them [15] to thermalize systems of size up to L = 12, very clear results were reached for the XY spin glasses. The finite-lattice correlation length [20], ξ L , was analyzed for several system sizes L. As expected [2,4,5], the dimensionless ratio ξ L /L crosses neatly at the same T c , for the chiral glass and the spin glass ordering, for XY spin glasses. In the more important case of Heisenberg spin glasses, their results, although inconclusive, were interpreted also as lack of spin-chirality decoupling. This conclusion has been criticized by Kawamura and Hukushima [14], that studied somehow larger systems on very few samples.Here we show that a finite-temperature spin glass transition occurs for the Heisenberg spin glass in D = 3. The critical temperature for the spin glass transition coincides with that of the chiral glass. Our results rely on Monte Carlo simulation and FSS analysis at T c [2,4,5]. We adapt a lattice gauge theory alg...

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“…A practical way around this problem is to consider only dimensionless ratios of the same quantity for different volume sizes at a fixed ratio. This idea is widely used in condensed matter applications, where scaling behavior in terms of a ratio of quantities at volumes of size L and 2L is considered [287,288,289]. Results for the ratio of correlation lengths ξ(2L)/ξ(L) as a function of the dimensionless ratio ξ(L)/L for an O(4) model in d = 3 from [30] are shown in Fig.…”

Section: Scaling Analysis Of Lattice Datamentioning

confidence: 99%

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

Klein

2017

Physics Reports

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Finite-volume effects in Quantum Chromodynamics (QCD) have been a subject of much theoretical interest for more than two decades. They are in particular important for the analysis and interpretation of QCD simulations on a finite, discrete space-time lattice. Most of these effects are closely related to the phenomenon of spontaneous breaking of the chiral flavor symmetry and the emergence of pions as light Goldstone bosons. These long-range fluctuations are strongly affected by putting the system into a finite box, and an analysis with different methods can be organized according to the interplay between pion mass and box size. The finite volume also affects critical behavior at the chiral phase transition in QCD. In the present review, I will be mainly concerned with modeling such finite volume effects as they affect the thermodynamics of the chiral phase transition for two quark flavors.I review recent work on the analysis of finite-volume effects which makes use of the quark-meson model for dynamical chiral symmetry breaking. To account for the effects of critical long-range fluctuations close to the phase transition, most of the calculations have been performed using non-perturbative Renormalization Group (RG) methods. I give an overview over the application of these methods to a finite volume. The method, the model and the results are put into the context of related work in random matrix theory for very small volumes, chiral perturbation theory for larger volumes, and related methods and approaches. They are applied towards the analysis of finite-volume effects in lattice QCD simulations and their interpretation, mainly in the context of the chiral phase transition for two quark flavors.

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Extrapolating Monte Carlo Simulations to Infinite Volume: Finite-Size Scaling atξ/L≫1

Cited by 105 publications

References 15 publications

Finite-Size Scaling in the Driven Lattice Gas

Finite-Size Scaling in the Driven Lattice Gas

Spin-Glass Transition of the Three-Dimensional Heisenberg Spin Glass

Modeling finite-volume effects and chiral symmetry breaking in two-flavor QCD thermodynamics

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