The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

Merdan, Ziya; Erdem, Rıza

doi:10.1016/j.physleta.2004.08.030

Cited by 28 publications

(27 citation statements)

References 34 publications

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“…For example, in discussing [10][11][12][13][14][15][16] how the finite-size-scaling behavior [17] changes for systems above the upper critical dimensionality, accurate estimates of the critical parameters are needed as benchmarks. Our data can also help to assess the accuracy of estimates of physical parameters obtained from approximations of a different nature, such as the the = 4 − d expansion [9,18] of the renormalization group * paolo.butera@mib.infn.it † mario.pernici@mi.infn.it theory, the fixed-dimension renormalization group [19], the 1/d expansion [6,8], the Monte Carlo (MC) simulations, etc.…”

Section: Introductionmentioning

confidence: 99%

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

Butera¹,

Pernici²

2012

Phys. Rev. E

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The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general d-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general d expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.

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Section: Introductionmentioning

confidence: 99%

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

Butera¹,

Pernici²

2012

Phys. Rev. E

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“…Among hundreds of subjects we can mention the study of finite size effects at first order transitions by gaussian approximation [7][8], the Gibbs ensemble [9], five dimensional Ising model [10][11], percolation models [12][13], stochastic sandpiles [14], six-dimensional Ising system [15], Baxter-Wu model [16], two dimensional anisotropic Heisenberg model [17]...…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation of finite size effects at DNA melting

Buyukdagli

Joyeux

2007

Phys. Rev. E

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We investigated how the finiteness of the length of the sequence affects the phase transition that takes place at DNA melting temperature. For this purpose, we modified the Transfer Integral method to adapt it to the calculation of both extensive (partition function, entropy, specific heat, etc) and non-extensive (order parameter and correlation length) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We showed that rounding of the transition clearly takes place when the length of the sequence is decreased. We also performed a finite-size scaling analysis of the two models and showed that the singular part of the free energy can indeed be expressed in terms of an homogeneous function. However, both the correlation length ξ and the average separation between paired bases y diverge at the melting transition, so that it is no longer clear to which of these two quantities the length L of the system should be compared. Moreover, Josephson's identity is satisfied for none of the investigated models, so that the derivation of the characteristic exponents which appear, for example, in the expression of the specific heat, requires some care.(♯)

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“…By considering different approximate methods, the approximations of the solutions of twodimensional ferromagnetic Ising model are presented [9][10][11][12][13]. In addition, the four-dimensional ferromagnetic Ising model solution is approximated by using Creutz cellular automaton algorithm with nearest neighbor interactions and near the critical region [14][15][16][17][18][19][20][21][22][23]. The algorithm of approximating finite size behavior of ferromagnetic Ising model is extended to higher dimensions [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the four-dimensional ferromagnetic Ising model solution is approximated by using Creutz cellular automaton algorithm with nearest neighbor interactions and near the critical region [14][15][16][17][18][19][20][21][22][23]. The algorithm of approximating finite size behavior of ferromagnetic Ising model is extended to higher dimensions [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. It is established that the algorithm has been powerful in terms of providing the values of static critical exponents near the critical region in four and higher dimensions with nearest neighbor interactions [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]…”

Section: Introductionmentioning

confidence: 99%

The Finite-Size Scaling Study of Five-Dimensional Ising Model

2016

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The five-dimensional ferromagnetic Ising model is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice is found to be T χ (∞) = 8.7811 (1) using 4 ≤ L ≤ 8 which is also in very good agreement with the precise result. The value of the field critical exponent (δ = 3.0067 (2)) is good agreement with δ = 3 which is obtained from scaling law of Widom. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.5080 (1), 2.5005 (3) and 1.2501 (1) using 4 ≤ L ≤ 8, respectively, which are in very good agreement with the theoretical predictions of . The finite-size scaling plots of magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinitelattice temperature.

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The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

Cited by 28 publications

References 34 publications

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

High-temperature expansions of the higher susceptibilities for the Ising model in general dimensiond

Theoretical investigation of finite size effects at DNA melting

The Finite-Size Scaling Study of Five-Dimensional Ising Model

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