Monte Carlo study of the Ising ferromagnet on the site-diluted triangular lattice

Najafi, M. N.

doi:10.1016/j.physleta.2015.11.014

Cited by 20 publications

(40 citation statements)

References 36 publications

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“…In contrast to Ref. [19], we see that c remains close to This result is confirmed indirectly by results of the Wolff cluster algorithm [25,27] indices for the site-diluted Ising model agree with those for the pure Ising model as it is shown in Ref. [24].…”

Section: Site-diluted Ising Modelsupporting

confidence: 77%

“…The site-diluted Ising model has a critical point for any given value of p. The critical temperature changes continuously with respect to p. There is a claim that the central charge should also depend on p [19]. In our study we found it not to be true.…”

Section: Site-diluted Ising Modelcontrasting

confidence: 68%

“…Using the symmetry arguments, one expects that the critical behavior is the same as in the pure Ising model with c = 1/2. But previous investigations have given contradictory results [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Determination of the conformal-field-theory central charge by the Wang-Landau algorithm

Belov¹,

Nazarov²,

Сорокин³

2017

Phys. Rev. E

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We propose a simple method to estimate the central charge of the conformal field theory corresponding to a critical point of a two-dimensional lattice model from Monte Carlo simulations. The main idea is to use the Wang-Landau flat-histogram algorithm, which allows us to obtain the free energy of a lattice model on a torus as a function of torus radii. The central charge is calculated with a good precision from a free energy scaling at the critical point. We apply the method to the Ising, tricritical Ising (Blume-Capel), Potts and site-diluted Ising models, and also discuss estimation of conformal weights.

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Section: Site-diluted Ising Modelsupporting

confidence: 77%

Section: Site-diluted Ising Modelcontrasting

confidence: 68%

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Determination of the conformal-field-theory central charge by the Wang-Landau algorithm

Belov¹,

Nazarov²,

Сорокин³

2017

Phys. Rev. E

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“…This indicates that the Ising-like behavior is preserved in the site-diluted model and the central charge is universal in contrast to results of Ref. [15].…”

Section: Introductioncontrasting

confidence: 81%

“…In contrast to Ref. [15], we see that c remains close to This result is confirmed indirectly by results of the Wolff cluster algorithm [21,19]. The right plot of Figure 1 shows that the values of the critical indices agree with those for the pure Ising model.…”

Section: Site-diluted Ising Model (P < 1)supporting

confidence: 70%

Numerical determination of the CFT central charge in the site-diluted Ising model

Belov

Nazarov

Сорокин

2017

J. Phys.: Conf. Ser.

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Abstract. We propose a new numerical method to determine the central charge of the conformal field theory models corresponding to the 2D lattice models. In this method, the free energy of the lattice model on the torus is calculated by the Wang-Landau algorithm and then the central charge is obtained from a free energy scaling with respect to the torus radii. The method is applied for determination of the central charge in the site-diluted Ising model.

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Critical density of topological defects upon a continuous phase transition

Сорокин

2019

Annals of Physics

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Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has an universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional models where domain walls, vortices, so-called Z 2 vortices or their combinations are presented. These topological defects are relevant correspondingly to an Ising second-order phase transition, a Berezinskii-Kosterlitz Thouless transition and an explicit crossover. We compare results for square and triangular lattices as well as for the complicated situation when two types of defects are presented and two transitions occur separated in temperature. All considered cases demonstrate consentient results confirming the hypothesis.

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Monte Carlo study of the Ising ferromagnet on the site-diluted triangular lattice

Cited by 20 publications

References 36 publications

Determination of the conformal-field-theory central charge by the Wang-Landau algorithm

Determination of the conformal-field-theory central charge by the Wang-Landau algorithm

Numerical determination of the CFT central charge in the site-diluted Ising model

Critical density of topological defects upon a continuous phase transition

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