aqora

a Dynamic Cluster Approximation for Second-Order Phase Transitions.

Koichiro Matsuno

Jan 1, 19720 citations

4a-D-4 On Orders of Phase Transitions in Cluster Approximations at the Ground State II

Y. Nonomura

Abstracts of the meeting of the Physical Society of Japan. Sectional meetingAug 16, 19940 citations

Clusters and phase transitions

Boris Michailovich Smirnov

Uspekhi Fizicheskih NaukJan 1, 200723 citations

A Model of Superconductors on a Lattice

Tohru Morita

We study a model fermion system on a lattice, which is expected to show the superconductor state, the normal state and the antiferromagnetic state, as we vary the number density of particles and the temperature. The phase transition between the superconductor state and the normal state is investigated in the “molecular-field approximation” with the aid of the cluster variation method.

Journal of the Physical Society of JapanNov 15, 19900 citations

A mean-field approach applied for the ferromagnetic spin-1 Blume-Capel model

J. Roberto Viana, Octavio D. Rodrı́guez Salmon, Minos A. Neto

We applied a mean-field approach associated to Monte Carlo simulations in order to study the spin-1 ferromagnetic Blume-Capel model in the square and the linear lattice. This new technique, which we call MFT-MC, determines the molecular field as the magnetization response of a Monte Carlo simulation. The resulting phase diagram is qualitatively correct, in contrast to effective-field approximations, in which the first-order line is not perpendicular to the anisotropy axis at low temperatures. Thermodynamic quantities, as the entropy and the specific heat curves can be obtained so as to analyze the nature of the phase transition points. Also, the possibility of using larger sizes constitutes an improvement regarding other mean-field approximations that use clusters.We applied a mean-field approach associated to Monte Carlo simulations in order to study the spin-1 ferromagnetic Blume-Capel model in the square and the linear lattice. This new technique, which we call MFT-MC, determines the molecular field as the magnetization response of a Monte Carlo simulation. The resulting phase diagram is qualitatively correct, in contrast to effective-field approximations, in which the first-order line is not perpendicular to the anisotropy axis at low temperatures. Thermodynamic quantities, as the entropy and the specific heat curves can be obtained so as to analyze the nature of the phase transition points. Also, the possibility of using larger sizes constitutes an improvement regarding other mean-field approximations that use clusters.

arXiv:1607.01270Jul 5, 20160 citations

Thermodynamics of six-vertex models in direct and staggered electric fields in the cluster approximation

Валентин Григорьевич Вакс, В. И. Зиненко

The thermodynamics of the six-vertex models in direct and staggered electric fields is investigated using the cluster field method. The scheme of the successive approximations of the method is described and the result of the first and second approximations are presented. The cluster field method is shown to combine simplicity with high accuracy, in particular, in the description of ferroelectric phase transitions where the basic results agree with the exact ones in all the exactly soluble cases. The properties of the models in the staggered field s not=0 are investigated in detail. The expressions obtained for the ferroelectric phase transition point T F (s) and for the polarisability near T F (s) are apparently exact for the six-vertex models.The thermodynamics of the six-vertex models in direct and staggered electric fields is investigated using the cluster field method. The scheme of the successive approximations of the method is described and the result of the first and second approximations are presented. The cluster field method is shown to combine simplicity with high accuracy, in particular, in the description of ferroelectric phase transitions where the basic results agree with the exact ones in all the exactly soluble cases. The properties of the models in the staggered field s not=0 are investigated in detail. The expressions obtained for the ferroelectric phase transition point T F (s) and for the polarisability near T F (s) are apparently exact for the six-vertex models.

Journal of Physics C Solid State PhysicsJun 20, 19866 citations

Phase transitions in a cluster molecular field approximation

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