On the Ising model for the simple cubic lattice

Häggkvist, Roland; Rosengren, Anders; Lundow, Per-Håkan; Markström, Klas; Andrén, Daniel; Kundrotas, Petras J.

doi:10.1080/00018730701577548

Cited by 39 publications

(63 citation statements)

References 36 publications

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“…The same tendency was found analysing the P(0) distributions of Ref. [20]. Using OBC, however, the logarithm of P(0) showed linear dependence only with respect to L 2k (see straight lines in Fig.…”

Section: Introductionsupporting

confidence: 58%

“…As in previous computations [4,5], we also tried to scale the ergodic relaxation time below the phase transition point using scaling argument x = Lє ν , where є = 1 -T/T c and ν is the critical exponent of the correlation length which for the 3D Ising model has the value in between 0.62 and 0.63 (see [19,20] and references therein). Assuming z = 2 and ν = 0.625 and using PBC we obtain that τ e is proportional to L z exp(const x 2 ) (see Fig.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On ergodic relaxation time in the three-dimensional Ising model

Grigalaits¹,

Lapinskas²,

Banys³

et al. 2013

Lith. J. Phys.

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We have studied the dynamical decay of the autocorrelation function of the 3D Ising model for different sizes L = 20-52 of spin cluster-cubes. The behaviour of the longest, ergodic relaxation time, τ e , of a finite domain below the phase transition temperature T c was mostly considered for two types of phase transition dynamics. A study of the scaling properties of τ e demonstrates a negligible difference between the types of dynamics used, but a considerable difference for different boundary conditions. In contrast to the known result for periodic boundary conditions (τ e ~ L z exp [const(Lє

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Section: Introductionsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

On ergodic relaxation time in the three-dimensional Ising model

Grigalaits¹,

Lapinskas²,

Banys³

et al. 2013

Lith. J. Phys.

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show abstract

“…[7,19]. For this purpose several sampling methods have been developed which make it possible to obtain data in the micro-canonical ensemble, such as the multi-canonical method [1,2], the multiple-range method in [3] and the variety of methods unified in [5].…”

Section: Discussionmentioning

confidence: 99%

Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

Lundow

Markström

2009

Open Physics

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Abstract:In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.

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“…A significant progress has been made in the development of numerical algorithms allowing successful investigation of critical characteristics [10][11][12][13] and energy spectra of spin systems [14]. The Monte Carlo approach [15,16], which permits rough estimations, is mostly used in this kind of algorithms.…”

Section: Introductionmentioning

confidence: 99%

Analytical expressions for a finite-size 2D Ising model

Karandashev

Kryzhanovsky

Malsagov

2017

Opt. Mem. Neural Networks

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Abstract. Numerical methods are used to examine the thermodynamic characteristics of the twodimensional Ising model as a function of the number of spins N. Onsager's solution is generalized to a finite-size lattice, and experimentally validated analytical expressions for the free energy and its derivatives are computed. The heat capacity at the critical point is shown to grow logarithmically with N. Due to the finite extent of the system the critical temperature can only be determined to some accuracy.

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On the Ising model for the simple cubic lattice

Cited by 39 publications

References 36 publications

On ergodic relaxation time in the three-dimensional Ising model

On ergodic relaxation time in the three-dimensional Ising model

Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

Analytical expressions for a finite-size 2D Ising model

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