Finite-size effects and phase transition in the three-dimensional three-state Potts model

We discuss finite-size effects in one disordered [Formula: see text] model defined in a [Formula: see text]-dimensional Euclidean space. We consider that the scalar field satisfies periodic boundary conditions in one dimension and it is coupled with a quenched random field. In order to obtain the average value of the free energy of the system, we use the replica method. We first discuss finite-size effects in the one-loop approximation in [Formula: see text] and [Formula: see text]. We show that in both cases, there is a critical length where the system develop a second-order phase transition, when the system presents long-range correlations with power-law decay. Next, we improve the above result studying the gap equation for the size-dependent squared mass, using the composite field operator method. We obtain again that the system present a second-order phase transition with long-range correlation with power-law decay.

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Improving the Accuracy of Multihole Probe Measurements in Velocity Gradients

Volume 2: Controls, Diagnostics and Instrumentation; Cycle Innovations; Electric Power ◽

10.1115/gt2008-50492 ◽

2008 ◽

Author(s):

Valery Chernoray ◽

Johan Hja¨rne

Keyword(s):

Size Effects ◽

Three Dimensional ◽

Finite Size ◽

Correction Method ◽

Single Step ◽

Streamwise Vorticity ◽

Finite Size Effects ◽

Good Efficiency ◽

Vorticity Component ◽

Crossflow Velocity

This study describes an implementation and verification of an effective and reliable correction for the finite-size effects of pressure probes. A modified version of correction by Ligrani et al. (Exp. Fluids, vol. 7, 1989, p. 424) was used. It is shown that the correction procedure can be implemented in two steps as in Ligrani et al. or in a single step, either for probe pressures, or for velocity components. The latter correction method is found to have the best performance and studied in very detail. The effect of the correction in application to the highly three-dimensional flow downstream of the outlet guide vanes is scrutinized through detailed side-by-side comparison with corresponding cross hot-wire data. The influence of the correction on all three velocity components, flow streamlines and streamwise vorticity fields is thoroughly examined. Two flow cases with different incoming turbulence intensities are considered. The study demonstrates a very good efficiency and reliability of the correction, which lead to a significant improvement of the corrected velocity data. The improvement in crossflow velocity components has allowed correct description of the flow streamlines, and as a result, the secondary flow field structures were resolved more accurately. The considered correction does not affect the streamwise vorticity component, which is clarified as well. A very important fact is that the correction is not found to over-correct and distort the data, thus can be used safely. A very good performance of the correction for the finite-size effects of pressure probes presented in this study allows us to recommend it as a mandatory step in postprocessing procedures for multihole pressure probes.

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Monte Carlo study of finite-size effects at a weakly first-order phase transition

Physical Review B ◽

10.1103/physrevb.39.11932 ◽

1989 ◽

Vol 39 (16) ◽

pp. 11932-11942 ◽

Cited By ~ 84

Author(s):

P. Peczak ◽

D. P. Landau

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Order Phase Transition ◽

Size Effects ◽

Finite Size ◽

Monte Carlo Study ◽

Finite Size Effects ◽

First Order ◽

First Order Phase Transition ◽

First Order Phase

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