On the critical temperature of a quasi-one-dimensional Ising model

Yurishchev, M. A.; Sterlin, A. M.

doi:10.1088/0953-8984/3/14/016

Cited by 7 publications

(6 citation statements)

References 15 publications

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“…Since we are able to perform the calculations for subsystems with n ≤ 4, this allows us to have two independent iterations, with (2, 3) and (3,4) pairs (a degenerate pair (1,2) was eliminated from the consideration due to its anomalies [17]). Two steps of converging iterations give already a possibility to extract valuable information about tendencies in the change of quantities with increasing n.…”

Section: Behavior Of the Critical Amplitude Ratiosmentioning

confidence: 99%

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Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model

Yurishchev

1997

Phys. Rev. E

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A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders nϫnϫϱ is investigated by the transfer-matrix finite-size-scaling method. In addition to the previously obtained critical amplitudes of the inverse correlation lengths and singular part of the free energy ͓M. A. Yurishchev, Phys. Rev. B 50, 13 533 ͑1994͔͒, the amplitudes of the usual ͑''linear''͒ and nonlinear susceptibilities and the amplitude of the second derivative of the spin-spin inverse correlation length with respect to the external field are calculated. The behavior of critical amplitude combinations ͑which, in accordance with the Privman-Fisher equations, do not contain in their composition the nonuniversal metric coefficients and geometry prefactor͒ are studied as a function of the interaction anisotropy parameters. A universality domain for the amplitude ratios is found in the quasi-one-dimensional regime of interactions in the system. In the case of a fully isotropic three-dimensional Ising model for which the high precision values of the critical coupling and critical-point free energy are available, improved estimates are obtained for the following four universal quantities: ͑1͒ the amplitude of spin-spin inverse correlation length, ͑2͒ the amplitude of singular part of the free energy, ͑3͒ the ratio of the amplitude of a second derivative of the spin-spin inverse correlation length with respect to the external field to the usual susceptibility amplitude, and ͑4͒ the ratio of the nonlinear susceptibility amplitude to the square of the linear susceptibility amplitude ͑i.e., for the finite-size counterpart of the four-point renormalized coupling constant͒. ͓S1063-651X͑97͒07303-0͔

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Section: Behavior Of the Critical Amplitude Ratiosmentioning

confidence: 99%

“…( 17) to the basis of the identity irreducible representation of the group T ∧ C 2v . Expansion (17) preserves the above form but now its terms are blocks corresponding to the indicated representation.…”

Section: Formulas For the Susceptibilities And For The Inverse Correl...mentioning

confidence: 99%

Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model

Yurishchev

1997

Phys. Rev. E

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“…and (ii) J x = J y , corresponding to the partly anisotropic three-dimensional Ising model for which there exists sufficiently accurate estimates of T c (Navarro andde Jongh 1978, Yurishchev andSterlin 1991).…”

Section: Cluster 3 × 3 × ∞mentioning

confidence: 99%

“…As a result, one can find the critical temperatures only up J x(y) /J z = 10 −2 (with exactness in the onetwo significant figure range). In the quasi-one-dimensional case, the phase transition temperature has been calculated also by phenomenological renormalisation of clusters (Yurishchev and Sterlin 1991). Inasmuch, the cluster geometry reflects the physical situation; this approach (contrary to the high-temperature series expansions) yields more precise results as the anisotropy of quasi-one-dimensional system increases.…”

Section: Introductionmentioning

confidence: 99%

The critical temperature of a fully anisotropic three-dimensional Ising model

Yurishchev¹

1993

J. Phys.: Condens. Matter

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Short title: Critical temperature of Ising model PACS number(s): 05.50, 75.10HAbstract. The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite size scaling for L × L × ∞ clusters (L = 2 and 3). The results obtained are compared with available calculations.An exact analytical solution is found for the 2×2×∞ Ising chain with fully anisotropic interactions (arbitrary J x , J y and J z ). K c = 0.221 6544 ± 0.000 0010 (Livet 1991). The efficiency of progress is less for the partly anisotropic model when J x = J y = J z . Two cases exist here: J x = J y ≥ J z (a quasi-two-dimensional model) and, inversely, J x = J y ≤ J z (a quasi-one-dimensional model). Using the hightemperature series, the critical temperature estimates have been obtained with 2 × 10 −2 % error for the fully isotropic interactions (J x = J y = J z ) and about 10 −3 % in the two-dimensional limit (J z = 0) of quasi-two-dimensional model (see Navarro and de Jongh 1978 and references cited there). By intermediate range of interlayer couplings, the error of a phase transition temperature determination lies between these two extreme values. Conversely, in the quasi-one-dimensional case, the estimates based on the same high-temperature series are rapidly deteriorated due to the limited number of terms available in the series. As a result, one can find the critical temperatures only up J x(y) /J z = 10 −2 (with exactness in the onetwo significant figure range).In the quasi-one-dimensional case, the phase transition temperature has been calculated also by phenomenological renormalisation of clusters . Inasmuch, the cluster geometry reflects the physical situation; this approach (contrary to the high-temperature series expansions) yields more precise results as the anisotropy of quasi-one-dimensional system increases. By J x(y) /J z = 10 −3 , the critical temperature position is determined here with an accuracy of about three significant figures. The difficulties are largest when the interactions are different along all three directions. Here there are the calculations done by real-space renormalisation group method (da Silva et al 1984) and the calculations carried out via various versions of mean field theory and variational principle (see Faleiro Ferreira 1988, 1989 and references therein). These results we discuss in detail in the third section in comparing with our computations.In this paper, the critical temperature of a three-dimensional Ising model, with

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“…The different influence of the various substitutions on the antiferromagnetic ordering can be understood qualitatively as follows. The three-dimensional ordering of Ising (as well as, e.g., Heisenberg or XXZ) spin chains requires a finite interchain coupling, but the actual value of T N depends only weakly on the interchain coupling 31,32 . Because the Sr substitution mainly changes the a axis, i.e.…”

Section: Low-field Measurementsmentioning

confidence: 99%

Substitution effects on the temperature vs. magnetic-field phase diagrams of the quasi-1D effective Ising spin-1/2 chain system BaCo$_2$V$_2$O$_8$

Niesen,

Breunig,

Salm

et al. 2014

Preprint

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BaCo2V2O8 is a one-dimensional antiferromagnetic spin-1/2 chain system with pronounced Ising anisotropy of the magnetic exchange. Due to finite interchain interactions long-range antiferromagnetic order develops below TN 5.5 K, which is accompanied by a structural distortion in order to lift magnetic frustration effects. The corresponding temperature vs. magnetic-field phase diagram is highly anisotropic with respect to the magnetic-field direction and various details are still under vivid discussion. Here, we report the influence of several substitutions on the magnetic properties and the phase diagrams of BaCo2V2O8. We investigate the substitution series Ba1-xSrxCo2V2O8 over the full range 0 ≤ x ≤ 1 as well as the influence of a partial substitution of the magnetic Co 2+ by small amounts of other magnetic transition metals or by non-magnetic magnesium. In all cases, the phase diagrams were obtained on single crystals from magnetization data and/or high-resolution studies of the thermal expansion and magnetostriction.

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On the critical temperature of a quasi-one-dimensional Ising model

Cited by 7 publications

References 15 publications

Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model

Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model

The critical temperature of a fully anisotropic three-dimensional Ising model

Substitution effects on the temperature vs. magnetic-field phase diagrams of the quasi-1D effective Ising spin-1/2 chain system BaCo$_2$V$_2$O$_8$

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