An Improved Linear Chain Approximation for the Free Energy

Ferreira, J. R. Faleiro

doi:10.1002/pssb.2221560228

Physica Status Solidi (b)

1989

DOI: 10.1002/pssb.2221560228

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An Improved Linear Chain Approximation for the Free Energy

J. R. Faleiro Ferreira¹

Abstract: Some previous results obtained through a new variational approach recently proposed can be improved by using a sum of linear chains ss the trial Hsmiltonian. That approximation preserves short-range order effects above the approximate critical temperature.Einige vorlllufige Ergebnisse, die mit einem neuen kurzlich vorgeschlagenen Variationsverfahren erhalten werden, lassen sich durch Benutzung einer Summe linearer Ketten als Versuchs-Hamiltonoperator verbessern. Diese Naherung bewahrt Nahordnungseffekte oberha… Show more

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A Weighted Linear Chain Approximation for the Ising Model Free Energy

Ferreira

Silva

Franco

1992

Physica Status Solidi (b)

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3D Ising model thermodynamic functions are evaluated through a variational approach in which the partition function is taken as product of different direction linear chain partition functions.Die thermodynamischen Funktionen des 3D-Isingmodells werden mittels eines Variationsverfahrens berechnet, bei dem die Verteilungsfunktion als Produkt von Verteilungsfunktionen hearer Ketten unterschiedlicher Richtung angenommen wird.

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A Weighted Linear Chain Approximation for the Ising Model Free Energy

Ferreira

Silva

Franco

1992

Physica Status Solidi (b)

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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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An Improved Linear Chain Approximation for the Free Energy

Cited by 2 publications

References 11 publications

A Weighted Linear Chain Approximation for the Ising Model Free Energy

A Weighted Linear Chain Approximation for the Ising Model Free Energy

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

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