Critical amplitude ratios of the Baxter–Wu model

Shchur, Lev N.; Janke, Wolfhard

doi:10.1016/j.nuclphysb.2010.07.016

Cited by 17 publications

(16 citation statements)

References 66 publications

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“…[76] preserving the second order character of the undilute case up to a critical value of the vacancy density, and becoming first order above this value (Fig. 10).…”

Section: Tablementioning

confidence: 94%

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Fields, particles and universality in two dimensions

Delfino

2015

Annals of Physics

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We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.Comment: 58 pages, 19 figures. Expanded notes of lectures given at the school "Statistical Field Theories", GGI Arcetri, Florence, February 2015; v2: references adde

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“…[76] preserving the second order character of the undilute case up to a critical value of the vacancy density, and becoming first order above this value (Fig. 10).…”

Section: Tablementioning

confidence: 94%

“…On universality grounds it is natural to identify (76) to the scattering solution of the scaling threestate Potts model, whose integrability we argued above. The identification is correct [48,49] and in this as in the other cases the ultimate check is provided by a technique known as thermodynamic Bethe ansatz [49].…”

Section: Purely Transmissive Scatteringmentioning

confidence: 99%

Fields, particles and universality in two dimensions

Delfino

2015

Annals of Physics

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“…We report in Table III the finite-size estimates of the critical exponent ν obtained from Eqs. (6) and (9), as well as the critical exponent η obtained from Eq. (9).…”

Section: Estimated Bymentioning

confidence: 99%

“…It should be said that further extensions of the spin-1/2 model given by Eq. (1) above have also been recently made by considering transverse [7] and longitudinal [8] magnetic fields, Monte Carlo studies of the critical amplitude ratios [9] and short-time dynamics [10], among several others.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field

2017

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The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.

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“…Often this provides a tool to improve accuracy of the MC estimation of critical exponents, especially in cases complicated by the presence of logarithmic corrections [14]. In particular, the studies of critical amplitudes of the specific heat expansions [15][16][17][18][19][20] and the studies of universal and non-universal features of certain combinations of critical amplitudes of the order parameter [20][21][22][23] are very interesting topics. One of the well-known generalizations of the Ising model is the S = 1 model studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Universality of the Ising and theS=1model on Archimedean lattices: A Monte Carlo determination

et al. 2012

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The Ising model S = 1/2 and the S = 1 model are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well known 2d Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S = 1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2d Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S = 1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.

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Critical amplitude ratios of the Baxter–Wu model

Cited by 17 publications

References 66 publications

Fields, particles and universality in two dimensions

Fields, particles and universality in two dimensions

Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field

Universality of the Ising and theS=1model on Archimedean lattices: A Monte Carlo determination

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