TY  - JOUR
AU  - Matić, Vladimir M.
AU  - Milošević, Sava
PY  - 1999
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2219
AB  - We have analyzed relationship between two parallel approaches to the cluster variation method (CVM) as a theoretical tool for studying statistical properties of binary systems. The first approach to the method uses the multisite correlation functions as variational variables, while the other approach is the one that uses the cluster effective fields as variational variables. Using the Ising model description of physical systems studied, we have shown that the two approaches should produce identical final results, although they deal with quite different systems of nonlinear equations (which, in particular cases under study, must be solved numerically for a given temperature and chemical potential). To achieve identical final results, we show that it is necessary to introduce cluster fields for those clusters which appear to be subclusters of at least two different members of the Kikuchi cluster family. In addition, we demonstrate that variational variables of the two approaches generate two sets of cluster probabilities, whose intersection contains solution of the CVM approximation which corresponds to the thermodynamic equilibrium state. We also analyze the existence of the so-called consistency relations in both approaches to the CVM method, and, finally, we discuss the problem of convergency of numerical procedures that are used to analyze the low-temperature states of the model systems under study. (C) 1999 Elsevier Science B.V. All rights reserved.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method
VL  - 262
IS  - 1-2
SP  - 215
EP  - 231
DO  - 10.1016/S0378-4371(98)00406-3
ER  - 

@article{
author = "Matić, Vladimir M. and Milošević, Sava",
year = "1999",
abstract = "We have analyzed relationship between two parallel approaches to the cluster variation method (CVM) as a theoretical tool for studying statistical properties of binary systems. The first approach to the method uses the multisite correlation functions as variational variables, while the other approach is the one that uses the cluster effective fields as variational variables. Using the Ising model description of physical systems studied, we have shown that the two approaches should produce identical final results, although they deal with quite different systems of nonlinear equations (which, in particular cases under study, must be solved numerically for a given temperature and chemical potential). To achieve identical final results, we show that it is necessary to introduce cluster fields for those clusters which appear to be subclusters of at least two different members of the Kikuchi cluster family. In addition, we demonstrate that variational variables of the two approaches generate two sets of cluster probabilities, whose intersection contains solution of the CVM approximation which corresponds to the thermodynamic equilibrium state. We also analyze the existence of the so-called consistency relations in both approaches to the CVM method, and, finally, we discuss the problem of convergency of numerical procedures that are used to analyze the low-temperature states of the model systems under study. (C) 1999 Elsevier Science B.V. All rights reserved.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method",
volume = "262",
number = "1-2",
pages = "215-231",
doi = "10.1016/S0378-4371(98)00406-3"
}

Matić, V. M.,& Milošević, S.. (1999). Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method. in Physica A: Statistical Mechanics and Its Applications, 262(1-2), 215-231.
https://doi.org/10.1016/S0378-4371(98)00406-3

Matić VM, Milošević S. Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method. in Physica A: Statistical Mechanics and Its Applications. 1999;262(1-2):215-231.
doi:10.1016/S0378-4371(98)00406-3 .

Matić, Vladimir M., Milošević, Sava, "Equivalence of two parallel approaches to the cluster variation method: the multisite correlation functions method and the cluster effective fields method" in Physica A: Statistical Mechanics and Its Applications, 262, no. 1-2 (1999):215-231,
https://doi.org/10.1016/S0378-4371(98)00406-3 . .

TY  - JOUR
AU  - Stošić, Tatijana
AU  - Stošić, Borko D.
AU  - Milošević, Sava
AU  - Stanley, Eugene H.
PY  - 1996
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2024
AB  - Owing to extremely slow decay of correlations, the limit H -- GT 0 presents a poor approximation for the Ising model on the Sierpinski gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite field induce an apparent phase transition, These observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Ising model on the Sierpinski gasket: Thermodynamic limit versus infinitesimal field
VL  - 233
IS  - 1-2
SP  - 31
EP  - 38
DO  - 10.1016/S0378-4371(96)00240-3
ER  - 

@article{
author = "Stošić, Tatijana and Stošić, Borko D. and Milošević, Sava and Stanley, Eugene H.",
year = "1996",
abstract = "Owing to extremely slow decay of correlations, the limit H -- GT 0 presents a poor approximation for the Ising model on the Sierpinski gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite field induce an apparent phase transition, These observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Ising model on the Sierpinski gasket: Thermodynamic limit versus infinitesimal field",
volume = "233",
number = "1-2",
pages = "31-38",
doi = "10.1016/S0378-4371(96)00240-3"
}

Stošić, T., Stošić, B. D., Milošević, S.,& Stanley, E. H.. (1996). Ising model on the Sierpinski gasket: Thermodynamic limit versus infinitesimal field. in Physica A: Statistical Mechanics and Its Applications, 233(1-2), 31-38.
https://doi.org/10.1016/S0378-4371(96)00240-3

Stošić T, Stošić BD, Milošević S, Stanley EH. Ising model on the Sierpinski gasket: Thermodynamic limit versus infinitesimal field. in Physica A: Statistical Mechanics and Its Applications. 1996;233(1-2):31-38.
doi:10.1016/S0378-4371(96)00240-3 .

Stošić, Tatijana, Stošić, Borko D., Milošević, Sava, Stanley, Eugene H., "Ising model on the Sierpinski gasket: Thermodynamic limit versus infinitesimal field" in Physica A: Statistical Mechanics and Its Applications, 233, no. 1-2 (1996):31-38,
https://doi.org/10.1016/S0378-4371(96)00240-3 . .