Finite-size scaling analysis of the critical behavior of the Baxter–Wu model

Martinos, S.S.; Malakis, A.; Hadjiagapiou, Ioannis A.

doi:10.1016/j.physa.2004.12.062

Cited by 23 publications

(41 citation statements)

References 27 publications

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“…In addition to the natural definition of the finite-volume transition point as the extrema of thermal susceptibility, χ T and specific heat c T , we have shown that the true finite-volume transition point manifests itself as a different particular point according to the quantity considered, namely as It is important to mention that the finite-volume transition point, using the connected Binder cumulant B c 4 (T, V ), is given by the little maximum B c 4 max between the two minima. By against, the minimum of the Binder cumulant B 4 (T, V ), (B 4 ) min as obtained in [19,36,55,56,58,59], is just a particular point and not the true finite-volume transition point. Obviously any particular point tends to the bulk transition point as V becomes large.…”

Section: Resultsmentioning

confidence: 90%

Finite-volume cumulant expansion in QCD-colorless plasma

et al. 2015

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Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point T 0 (V ) of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the L mn -method. The first six cumulants C 1,2,3,4,5,6 with the corresponding under-normalized ratios (skewness , kurtosis κ, pentosis Π ± , and hexosis H 1,2,3 ) and three unnormalized combinations of them, (O = σ 2 κ −1 , U = σ −2 −1 , N = σ 2 κ) are calculated and studied as functions of (T, V ). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value T 0 (V ) agrees with that expected T N 0 (V ) from the order parameter and the thermal susceptibility χ T (T, V ), according to the standard procedure of localization to within about 2 %. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.

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Section: Resultsmentioning

confidence: 90%

Finite-volume cumulant expansion in QCD-colorless plasma

et al. 2015

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“…The Baxter-Wu [42,43,44] and four-state Potts models in 2D [45] are well-known examples of such systems undergoing, in the thermodynamic limit, second-order phase transitions. Recently, Behringer and Pleimling [46] have demonstrated for these two models that, the appearance of a convex dip in the microcanonical entropy can be traced back to a finite-size effect different from what is expected in a genuine first-order transition.…”

Section: Introductionmentioning

confidence: 99%

First-order transition features of the 3D bimodal random-field Ising model

2008

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Abstract. Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal (±h) random-field Ising model at the strong disorder regime. We consider simple cubic lattices with linear sizes in the range L = 4 − 32 and simulate the system for two values of the disorder strength: h = 2 and h = 2.25. The nature of the transition is elucidated by applying the Lee-Kosterlitz free-energy barrier method. Our results indicate that, despite the strong first-order-like characteristics, the transition remains continuous, in disagreement with the early mean-field theory prediction of a tricritical point at high values of the random-field.

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“…[25] the short-time dynamics of the model has been investigated through the relaxation of the order parameter at the critical temperature. Finally, in relatively recent papers [26][27][28] Martinos et al have studied the behavior of the magnetization distribution function as well as other properties of the model at its first and second order phase transitions.…”

Section: Model and Methodsmentioning

confidence: 99%