TY  - JOUR
AU  - Stošić, Borko D.
AU  - Stošić, Tatijana
AU  - Fittipaldi, Ivon P.
PY  - 2005
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2911
AB  - While the Ising model on the Cayley tree has no spontaneous magnetization at nonzero temperatures in the thermodynamic limit, we show that finite systems of astronomical sizes remain magnetically ordered in a wide temperature range, if the symmetry is broken by fixing an arbitrary single (bulk or surface) spin. We compare the behavior of the finite size magnetization of this model with that of the [sing model on both the Sierpinski gasket, and the one-dimensional linear chain. This comparison reveals the analogy of the behavior of the present model with the Sierpinski gasket case. (c) 2005 Elsevier B.V. All rights reserved.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Thermodynamic limit for the Ising model on the Cayley tree
VL  - 355
IS  - 2-4
SP  - 346
EP  - 354
DO  - 10.1016/j.physa.2005.01.039
ER  - 

@article{
author = "Stošić, Borko D. and Stošić, Tatijana and Fittipaldi, Ivon P.",
year = "2005",
abstract = "While the Ising model on the Cayley tree has no spontaneous magnetization at nonzero temperatures in the thermodynamic limit, we show that finite systems of astronomical sizes remain magnetically ordered in a wide temperature range, if the symmetry is broken by fixing an arbitrary single (bulk or surface) spin. We compare the behavior of the finite size magnetization of this model with that of the [sing model on both the Sierpinski gasket, and the one-dimensional linear chain. This comparison reveals the analogy of the behavior of the present model with the Sierpinski gasket case. (c) 2005 Elsevier B.V. All rights reserved.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Thermodynamic limit for the Ising model on the Cayley tree",
volume = "355",
number = "2-4",
pages = "346-354",
doi = "10.1016/j.physa.2005.01.039"
}

Stošić, B. D., Stošić, T.,& Fittipaldi, I. P.. (2005). Thermodynamic limit for the Ising model on the Cayley tree. in Physica A: Statistical Mechanics and Its Applications, 355(2-4), 346-354.
https://doi.org/10.1016/j.physa.2005.01.039

Stošić BD, Stošić T, Fittipaldi IP. Thermodynamic limit for the Ising model on the Cayley tree. in Physica A: Statistical Mechanics and Its Applications. 2005;355(2-4):346-354.
doi:10.1016/j.physa.2005.01.039 .

Stošić, Borko D., Stošić, Tatijana, Fittipaldi, Ivon P., "Thermodynamic limit for the Ising model on the Cayley tree" in Physica A: Statistical Mechanics and Its Applications, 355, no. 2-4 (2005):346-354,
https://doi.org/10.1016/j.physa.2005.01.039 . .

TY  - JOUR
AU  - Stošić, Tatijana
AU  - Stošić, Borko D.
AU  - Moreira, Francisco George Brady
PY  - 1998
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2159
AB  - In this paper we use a diagrammatic technique to determine the exact recursion relations for the partition function of the Ising model in an external magnetic field, situated on the first two members of the checkerboard family of fractal lattices embedded in two dimensions. This represents the first exact general solution of this model for the case of nonzero field. The closed-form expression for the partition function is obtained for the first member in the zero-field limit and the nonzero-field recursion relations prove sufficient for exact evaluation of the response functions. We also calculate the temperature dependence of the specific heat and susceptibility.
T2  - Physical Review E
T1  - Exact solution of the Ising model on checkerboard fractals in an external magnetic field
VL  - 58
IS  - 1
SP  - 80
EP  - 85
DO  - 10.1103/PhysRevE.58.80
ER  - 

@article{
author = "Stošić, Tatijana and Stošić, Borko D. and Moreira, Francisco George Brady",
year = "1998",
abstract = "In this paper we use a diagrammatic technique to determine the exact recursion relations for the partition function of the Ising model in an external magnetic field, situated on the first two members of the checkerboard family of fractal lattices embedded in two dimensions. This represents the first exact general solution of this model for the case of nonzero field. The closed-form expression for the partition function is obtained for the first member in the zero-field limit and the nonzero-field recursion relations prove sufficient for exact evaluation of the response functions. We also calculate the temperature dependence of the specific heat and susceptibility.",
journal = "Physical Review E",
title = "Exact solution of the Ising model on checkerboard fractals in an external magnetic field",
volume = "58",
number = "1",
pages = "80-85",
doi = "10.1103/PhysRevE.58.80"
}

Stošić, T., Stošić, B. D.,& Moreira, F. G. B.. (1998). Exact solution of the Ising model on checkerboard fractals in an external magnetic field. in Physical Review E, 58(1), 80-85.
https://doi.org/10.1103/PhysRevE.58.80

Stošić T, Stošić BD, Moreira FGB. Exact solution of the Ising model on checkerboard fractals in an external magnetic field. in Physical Review E. 1998;58(1):80-85.
doi:10.1103/PhysRevE.58.80 .

Stošić, Tatijana, Stošić, Borko D., Moreira, Francisco George Brady, "Exact solution of the Ising model on checkerboard fractals in an external magnetic field" in Physical Review E, 58, no. 1 (1998):80-85,
https://doi.org/10.1103/PhysRevE.58.80 . .

TY  - JOUR
AU  - Stošić, Tatijana
AU  - Stošić, Borko D.
AU  - Fittipaldi, Ivon P.
PY  - 1998
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6230
AB  - We establish an exact expression, in closed form, for the zero-field susceptibility of the Ising model on a Cayley tree of arbitrary generation. We use the known exact recursion relations for the partition function to find the corresponding recursion relations for its field derivatives. These relations are then iterated for the zero-held case to yield the expression for the zero-field susceptibility. In the thermodynamic limit, our formula displays behavior in agreement with previous works. (C) 1998 Elsevier Science B.V. All rights reserved.
T2  - Journal of Magnetism and Magnetic Materials
T1  - Exact zero-field susceptibility of the Ising model on a Cayley tree
VL  - 177
SP  - 185
EP  - 187
DO  - 10.1016/S0304-8853(97)00329-6
ER  - 

@article{
author = "Stošić, Tatijana and Stošić, Borko D. and Fittipaldi, Ivon P.",
year = "1998",
abstract = "We establish an exact expression, in closed form, for the zero-field susceptibility of the Ising model on a Cayley tree of arbitrary generation. We use the known exact recursion relations for the partition function to find the corresponding recursion relations for its field derivatives. These relations are then iterated for the zero-held case to yield the expression for the zero-field susceptibility. In the thermodynamic limit, our formula displays behavior in agreement with previous works. (C) 1998 Elsevier Science B.V. All rights reserved.",
journal = "Journal of Magnetism and Magnetic Materials",
title = "Exact zero-field susceptibility of the Ising model on a Cayley tree",
volume = "177",
pages = "185-187",
doi = "10.1016/S0304-8853(97)00329-6"
}

Stošić, T., Stošić, B. D.,& Fittipaldi, I. P.. (1998). Exact zero-field susceptibility of the Ising model on a Cayley tree. in Journal of Magnetism and Magnetic Materials, 177, 185-187.
https://doi.org/10.1016/S0304-8853(97)00329-6

Stošić T, Stošić BD, Fittipaldi IP. Exact zero-field susceptibility of the Ising model on a Cayley tree. in Journal of Magnetism and Magnetic Materials. 1998;177:185-187.
doi:10.1016/S0304-8853(97)00329-6 .

Stošić, Tatijana, Stošić, Borko D., Fittipaldi, Ivon P., "Exact zero-field susceptibility of the Ising model on a Cayley tree" in Journal of Magnetism and Magnetic Materials, 177 (1998):185-187,
https://doi.org/10.1016/S0304-8853(97)00329-6 . .

TY  - JOUR
AU  - da Silva, Eronildes Felisberto
AU  - Stošić, Borko D.
PY  - 1997
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2081
AB  - To gain a better understanding of the silicon oxidation process, we perform numerical simulation of thermal SiO2 thin-film growth. It is shown that the oxidation rate in the early stages of growth is governed by two processes: the rapid initial formation of the oxidation front and its subsequent diffusion. The resulting oxidation rate provides a rather good description of the experimental data with the minimum number of variable parameters, suggesting that the effect of external parameters (such as temperature and pressure) can be explained in terms of scaling concepts. The results of the simulation are also in agreement with the fitting of experimental data to a power law x(ox)=s+at(b) (where x(ox) is the measured SiO2 film thickness and t the oxidation time) predicted by a simple model for thin SiO2 film growth.
T2  - Semiconductor Science and Technology
T1  - Simulation of the early stages of thin SiO2 film growth
VL  - 12
IS  - 8
SP  - 1038
EP  - 1045
DO  - 10.1088/0268-1242/12/8/018
ER  - 

@article{
author = "da Silva, Eronildes Felisberto and Stošić, Borko D.",
year = "1997",
abstract = "To gain a better understanding of the silicon oxidation process, we perform numerical simulation of thermal SiO2 thin-film growth. It is shown that the oxidation rate in the early stages of growth is governed by two processes: the rapid initial formation of the oxidation front and its subsequent diffusion. The resulting oxidation rate provides a rather good description of the experimental data with the minimum number of variable parameters, suggesting that the effect of external parameters (such as temperature and pressure) can be explained in terms of scaling concepts. The results of the simulation are also in agreement with the fitting of experimental data to a power law x(ox)=s+at(b) (where x(ox) is the measured SiO2 film thickness and t the oxidation time) predicted by a simple model for thin SiO2 film growth.",
journal = "Semiconductor Science and Technology",
title = "Simulation of the early stages of thin SiO2 film growth",
volume = "12",
number = "8",
pages = "1038-1045",
doi = "10.1088/0268-1242/12/8/018"
}

da Silva, E. F.,& Stošić, B. D.. (1997). Simulation of the early stages of thin SiO2 film growth. in Semiconductor Science and Technology, 12(8), 1038-1045.
https://doi.org/10.1088/0268-1242/12/8/018

da Silva EF, Stošić BD. Simulation of the early stages of thin SiO2 film growth. in Semiconductor Science and Technology. 1997;12(8):1038-1045.
doi:10.1088/0268-1242/12/8/018 .

da Silva, Eronildes Felisberto, Stošić, Borko D., "Simulation of the early stages of thin SiO2 film growth" in Semiconductor Science and Technology, 12, no. 8 (1997):1038-1045,
https://doi.org/10.1088/0268-1242/12/8/018 . .

TY  - JOUR
AU  - Stošić, Borko D.
AU  - Stošić, Tatijana
AU  - Fittipaldi, Ivon P.
AU  - Veerman, J.J.P.
PY  - 1997
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2071
AB  - We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.
T2  - Journal of Physics. A: Mathematical and General
T1  - Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix
VL  - 30
IS  - 10
SP  - L331
EP  - L337
DO  - 10.1088/0305-4470/30/10/006
ER  - 

@article{
author = "Stošić, Borko D. and Stošić, Tatijana and Fittipaldi, Ivon P. and Veerman, J.J.P.",
year = "1997",
abstract = "We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.",
journal = "Journal of Physics. A: Mathematical and General",
title = "Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix",
volume = "30",
number = "10",
pages = "L331-L337",
doi = "10.1088/0305-4470/30/10/006"
}

Stošić, B. D., Stošić, T., Fittipaldi, I. P.,& Veerman, J.J.P.. (1997). Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix. in Journal of Physics. A: Mathematical and General, 30(10), L331-L337.
https://doi.org/10.1088/0305-4470/30/10/006

Stošić BD, Stošić T, Fittipaldi IP, Veerman J. Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix. in Journal of Physics. A: Mathematical and General. 1997;30(10):L331-L337.
doi:10.1088/0305-4470/30/10/006 .

Stošić, Borko D., Stošić, Tatijana, Fittipaldi, Ivon P., Veerman, J.J.P., "Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix" in Journal of Physics. A: Mathematical and General, 30, no. 10 (1997):L331-L337,
https://doi.org/10.1088/0305-4470/30/10/006 . .

TY  - CONF
AU  - Stošić, Borko D.
AU  - Stošić, Tatijana
PY  - 1997
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2058
C3  - Journal of Applied Physics
T1  - Ising model on the Cayley tree: Finite size versus finite field
VL  - 81
IS  - 8
SP  - 4160
EP  - 4160
DO  - 10.1063/1.365052
ER  - 

@conference{
author = "Stošić, Borko D. and Stošić, Tatijana",
year = "1997",
journal = "Journal of Applied Physics",
title = "Ising model on the Cayley tree: Finite size versus finite field",
volume = "81",
number = "8",
pages = "4160-4160",
doi = "10.1063/1.365052"
}

Stošić, B. D.,& Stošić, T.. (1997). Ising model on the Cayley tree: Finite size versus finite field. in Journal of Applied Physics, 81(8), 4160-4160.
https://doi.org/10.1063/1.365052

Stošić BD, Stošić T. Ising model on the Cayley tree: Finite size versus finite field. in Journal of Applied Physics. 1997;81(8):4160-4160.
doi:10.1063/1.365052 .

Stošić, Borko D., Stošić, Tatijana, "Ising model on the Cayley tree: Finite size versus finite field" in Journal of Applied Physics, 81, no. 8 (1997):4160-4160,
https://doi.org/10.1063/1.365052 . .

TY  - JOUR
AU  - Stošić, Borko D.
AU  - Sastry, Srikanth
AU  - Kostić, Dragan
AU  - Milošević, Sava
AU  - Stanley, Eugene H.
PY  - 1996
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2017
AB  - We describe a geometric approach for studying phase transitions, based upon the analysis of the density of states (DOS) functions (exact partition functions) for finite Ising systems. This approach presents a complementary method to the standard Monte Carlo method, since with a single calculation of the density of states (which is independent of parameters and depends only on the topology of the system), the entire range of parameter values can be studied with minimal additional effort. We calculate the DOS functions for the nearest-neighbor (nn) Ising model in nonzero field for square lattices up to 12 x 12 spins, and for triangular lattices up to 12 spins in the base; this work significantly extends previous exact calculations of the partition function in nonzero field (8 x 8 spins for the square lattice). To recognize features of the DOS functions that correspond to phase transitions, we compare them with the DOS functions for the Ising chain and for the Ising model defined on a Sierpinski gasket. The DOS functions define a surface with respect to the dimensionless independent energy and magnetization variables; this surface is convex with respect to magnetization in the low-energy region for systems displaying a second-order phase transition. On the other hand, for systems for which there is no phase transition, the DOS surfaces are concave. We show that this geometrical property of the DOS functions is generally related to the existence of phase transitions, thereby providing a graphic tool for exploring various features of phase transitions. For each given temperature and field, we also define a free energy surface, from which we obtain the most probable energy and magnetization. We test this method of free energy surfaces on Ising systems with both nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions for various values of the ratio R = J(1)/J(2). For one particular choice, R = -0.1, we show how the free energy surface may be utilized to discern a first-order phase transition. We also carry out Monte Carlo simulations and compare these quantitatively with our results for the phase diagram.
T2  - Physica A: Statistical Mechanics and Its Applications
T1  - Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions
VL  - 232
IS  - 1-2
SP  - 349
EP  - 368
DO  - 10.1016/0378-4371(96)00239-7
UR  - https://hdl.handle.net/21.15107/rcub_vinar_2017
ER  - 

@article{
author = "Stošić, Borko D. and Sastry, Srikanth and Kostić, Dragan and Milošević, Sava and Stanley, Eugene H.",
year = "1996",
abstract = "We describe a geometric approach for studying phase transitions, based upon the analysis of the density of states (DOS) functions (exact partition functions) for finite Ising systems. This approach presents a complementary method to the standard Monte Carlo method, since with a single calculation of the density of states (which is independent of parameters and depends only on the topology of the system), the entire range of parameter values can be studied with minimal additional effort. We calculate the DOS functions for the nearest-neighbor (nn) Ising model in nonzero field for square lattices up to 12 x 12 spins, and for triangular lattices up to 12 spins in the base; this work significantly extends previous exact calculations of the partition function in nonzero field (8 x 8 spins for the square lattice). To recognize features of the DOS functions that correspond to phase transitions, we compare them with the DOS functions for the Ising chain and for the Ising model defined on a Sierpinski gasket. The DOS functions define a surface with respect to the dimensionless independent energy and magnetization variables; this surface is convex with respect to magnetization in the low-energy region for systems displaying a second-order phase transition. On the other hand, for systems for which there is no phase transition, the DOS surfaces are concave. We show that this geometrical property of the DOS functions is generally related to the existence of phase transitions, thereby providing a graphic tool for exploring various features of phase transitions. For each given temperature and field, we also define a free energy surface, from which we obtain the most probable energy and magnetization. We test this method of free energy surfaces on Ising systems with both nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions for various values of the ratio R = J(1)/J(2). For one particular choice, R = -0.1, we show how the free energy surface may be utilized to discern a first-order phase transition. We also carry out Monte Carlo simulations and compare these quantitatively with our results for the phase diagram.",
journal = "Physica A: Statistical Mechanics and Its Applications",
title = "Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions",
volume = "232",
number = "1-2",
pages = "349-368",
doi = "10.1016/0378-4371(96)00239-7",
url = "https://hdl.handle.net/21.15107/rcub_vinar_2017"
}

Stošić, B. D., Sastry, S., Kostić, D., Milošević, S.,& Stanley, E. H.. (1996). Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions. in Physica A: Statistical Mechanics and Its Applications, 232(1-2), 349-368.
https://doi.org/10.1016/0378-4371(96)00239-7
https://hdl.handle.net/21.15107/rcub_vinar_2017

Stošić BD, Sastry S, Kostić D, Milošević S, Stanley EH. Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions. in Physica A: Statistical Mechanics and Its Applications. 1996;232(1-2):349-368.
doi:10.1016/0378-4371(96)00239-7
https://hdl.handle.net/21.15107/rcub_vinar_2017 .

Stošić, Borko D., Sastry, Srikanth, Kostić, Dragan, Milošević, Sava, Stanley, Eugene H., "Geometric criteria for phase transitions: The Ising model with nearest and next-nearest neighbor interactions" in Physica A: Statistical Mechanics and Its Applications, 232, no. 1-2 (1996):349-368,
https://doi.org/10.1016/0378-4371(96)00239-7 .,
https://hdl.handle.net/21.15107/rcub_vinar_2017 .

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 . .