Monte Carlo analysis of the extended Ashkin-Teller model

Pawlicki, P.; Kamieniarz, G.; ̧bski, L. De

doi:10.1016/s0378-4371(97)00124-6

Cited by 16 publications

(12 citation statements)

References 20 publications

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“…The MFRG results [4] and the Monte Carlo simulations [5] do not confirm the existence of the tricritical points in the phase diagram of the EAT model which were present in the diagram calculated within MFA. Thus there is the problem of continuous transitions for the SAT model in 3D.…”

Section: Introductionmentioning

confidence: 65%

“…If the third-order terms are included [3,4], we obtain the extended Ashkin-Teller (EAT) model, which is described by the Hamiltonian (2) The SAT model corresponds to K = 0. The properties of the EAT model were investigated within the molecular-field approximation (MFA) [3], as well as in two dimensions (2D) also within the molecular field renormalization group (MFRG) method [4] and the Monte Carlo (MC) method [5], The SAT model in 2D and 3D was examined [6,7] within the Monte Carlo methods and the short series analysis, yielding approximate phase diagrams.…”

Section: Introductionmentioning

confidence: 99%

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Methods of Computer Simulations of Phase Transitions in the Ashkin-Teller Model

Musiał¹,

Dębski²,

Kamieniarz³

et al. 2001

CMST

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The complementary Monte Carlo and series expansions methods of computer simulations have been described to investigate the critical behaviour of the Ashkin-Teller model in three dimensions. In the first method the invariance of the ratio of the square of the second moment of the order parameter to its fourth moment in the critical region has been exploited and some critical points on the phase boundaries have been calculated in the regions where the continuous transitions are expected. The continuity of the order parameter on the critical lines is verified by a finite size scaling analysis. Large-scale simulations have been performed on SGI Power Challenge XL and L supercomputers using the 64-bit random number generator. The numerically generated series expansions method is described for which the effective algorithm for generation of graphs starting from polygons and based on collapsing the unlinked vertices, is introduced. The new feature of our algorithm is that for each graph we introduce new links between unlinked vertices and we decorate bonds with new vertices, so that more complex graphs in an early stage of the graph generation procedure are obtained. The resulting set of graphs enables the application of the series expansions method and achievement of the precision of allocation of points on the phase diagram comparable to the precision of the Monte Carlo method, i.e. at least 3 decimal digits.

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Section: Introductionmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Methods of Computer Simulations of Phase Transitions in the Ashkin-Teller Model

Musiał¹,

Dębski²,

Kamieniarz³

et al. 2001

CMST

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“…The transition point was determined [7,8] from the analysis of the fourth order cumulant where (Μn ) denotes the n-th power of an order parameter averaged over the assembly of independent samples of the size L x L or L x L x L in 2D and 3D, respectively. For Τ > Τ and L , where ξ denotes the correlation length, QL tends towards 1/3 which corresponds to a Gaussian distribution.…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…This behaviour of the cumulant is useful for determination of Τ. One may plot QL versus Τ for various L and estimate Τ from the intersection point of these curves [7].…”

Section: Description Of the Methodsmentioning

confidence: 99%

Monte Carlo Simulations of the Ashkin-Teller Model

Dębski

2000

Acta Phys. Pol. A

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Monte Carlo simulations are used to analyse the behaviour of the exteuded Ashkin-Teller model in two (2D) and three (3D) dimensions from the ratio of the square of the second moment of the order parameter to its fourth moment. The critical surface in three dimensional parameter space is calculated in regions where the Ising transitions are expected both for the ferro-and antiferromagnetic regions.

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“…The Monte Carlo method for sampling of the Gibbs distribution involves an element of chance [6,7]. Random (or, more strictly, pseudorandom) numbers are used to select the configurations of the system.…”

Section: The Methods Of Visualizationmentioning

confidence: 99%