Influence of an external field on the critical behavior of the 3D Ising-like model

Kozlovskii, M. P.; Romanik, R. V.

doi:10.1016/j.molliq.2011.12.003

Cited by 17 publications

(17 citation statements)

References 15 publications

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“…Using the representation of the GPF in the form of Eq. (4.5) the coexistence curve and the spinodal in temperature-magnetization coordinates was obtained in [25,26]. However, further use of all these results in description of the phase transition in fluid systems need additional calculations.…”

Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 89%

“…Thus the results obtained in [22] can be used here. Behavior of the order parameter was studied in the set of following works [23,24] As a result the state equation of the Ising-like model in the external field was obtained. Using the representation of the GPF in the form of Eq.…”

Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 99%

“…However, further use of all these results in description of the phase transition in fluid systems need additional calculations. Despite the similarity of expressions for the partition function of the Ising model in the external field [22,23,24,25,26] and the GPF of a fluid Eq. (4.5), there is a main difference in calculating the state equation of systems mentioned above.…”

Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 99%

“…We can deal with Eq. (3.18), using the method to calculate the GPF of the Ising model in external field proposed in [21]. In the present case the value h = βµ − βµ * (1 + τ ) − a 1 plays the role of the external field.…”

Section: So Introducing the Cell Model We Conditionally Divide Volumementioning

confidence: 98%

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Representation of the grand partition function of the cell model: The state equation in the mean-field approximation

Kozlovskii

Dobush

2016

Journal of Molecular Liquids

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The method to calculate the grand partition function of a particle system, in which constituents interact with each other via potential, that include repulsive and attractive components, is proposed. The cell model, which was introduced to describe critical phenomena and phase transitions, is used to provide calculations. The exact procedure of integration over particle coordinates and summation over number of particles is proposed. As a result, an evident expression for the grand partition function of the fluid cell model is obtained in the form of multiple integral over collective variables. As it can be seen directly from the structure of the transition jacobian, the present multiparticle model appeared to be different from the Ising model, which is widely used to describe fluid systems. The state equation, which is valid for wide temperature ranges both above and below the critical one, is derived in mean-field approximation. The pressure calculated for the cell model at temperatures above the critical one is found to be continuously increasing function of temperature and density. The isotherms of pressure as a function of density have horizontal parts at temperatures below the critical one.

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Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 89%

Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 99%

Section: The Grand Partition Function and Thermodynamic Characteristicsmentioning

confidence: 99%

Section: So Introducing the Cell Model We Conditionally Divide Volumementioning

confidence: 98%

See 2 more Smart Citations

Representation of the grand partition function of the cell model: The state equation in the mean-field approximation

Kozlovskii

Dobush

2016

Journal of Molecular Liquids

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“…[2][3][4][5][6][7] In this model, spins are treated as unit vectors assuming only discrete values of +1 and 1. A common choice in the literature is to consider nearest-neighbor interaction between spins.…”

Section: Introductionmentioning

confidence: 99%

A quantum simulation approach for a three-dimensional Ising spin model—Comparison to mean field theory

Liu

Ciftja

2017

AIP Advances

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We use a recently developed quantum simulation approach to study the properties of a three-dimensional Ising model consisting of S = 1/2 quantum spins localized at the sites of a simple cubic lattice. We assume nearest-neighbor interaction between spins with an exchange interaction that can be either ferromagnetic or antiferromagnetic. It is found that the computational method quickly converges towards the expected equilibrium spin configurations. The resulting spontaneous magnetization curves corresponding to the two types of magnetic interactions under consideration were found to be almost identical to the ones obtained via quantum mean field theory at all temperatures. The derived total energies, total free energies, magnetic entropies and specific heats per mole of spins show no sizeable differences from known theoretical values. Furthermore, the results of the simulations for two different 3D Ising systems containing 4×4×4 and 20×20×20 spins localized at the sites of a simple cubic lattice were found to be almost identical to each other. This finding suggests that the self-consistent algorithm approach of the current simulation method allows one to obtain the physical bulk properties of a large magnetic system by relying on simulations of a much smaller spin system sample. Therefore, the method presently considered appears to be not only very accurate as gauged by comparison to mean field theory, but also able to greatly increase the speed of simulations.

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Kinetics of a hydrolysis reaction in critical surfynol465/n-butanol/ethyl acetate/water microemulsion

Wang

Jin

Tan

et al. 2016

Journal of Molecular Liquids

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Influence of an external field on the critical behavior of the 3D Ising-like model

Cited by 17 publications

References 15 publications

Representation of the grand partition function of the cell model: The state equation in the mean-field approximation

Representation of the grand partition function of the cell model: The state equation in the mean-field approximation

A quantum simulation approach for a three-dimensional Ising spin model—Comparison to mean field theory

Kinetics of a hydrolysis reaction in critical surfynol465/n-butanol/ethyl acetate/water microemulsion

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