The method for calculation of the correlation functions of the Ising-type systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin $S^z=\pm1$ ) the expressions for pair and ternary correlation functions within two-particle approximation in $\set{q}$ -space are obtained for the hypercubic Bravais lattices. In the 1D case the exact expressions for them in the site space is obtained as well. On the basis of the Glauber equation within two-particle cluster approximation the longitudinal dynamical susceptibility $χ(\set{q},E)$ is found. In the 1D case and in the absence of external field the expression for $χ(\set{q},E)$ is exact. For the Emery-Blume-Griffiths model ( $S^z=-2,0,2$ ) within two-particle approximation the pair correlation functions are calculated. The four-particle cluster approximation is used for calculation of static susceptibility $χ(\set{q})$ of $KD_2PO_4$ ferroelectrics.The method for calculation of the correlation functions of the Ising-type systems with short-range interaction and with arbitrary value of spin is developed within cluster approximation. For the Ising model (spin $S^z=\pm1$) the expressions for pair and ternary correlation functions within two-particle approximation in $\set{q}$-space are obtained for the hypercubic Bravais lattices. In the 1D case the exact expressions for them in the site space is obtained as well. On the basis of the Glauber equation within two-particle cluster approximation the longitudinal dynamical susceptibility $χ(\set{q},E)$ is found. In the 1D case and in the absence of external field the expression for $χ(\set{q},E)$ is exact. For the Emery-Blume-Griffiths model ($S^z=-2,0,2$) within two-particle approximation the pair correlation functions are calculated. The four-particle cluster approximation is used for calculation of static susceptibility $χ(\set{q})$ of $KD_2PO_4$ ferroelectrics.

arXiv:cond-mat/9606134Jun 18, 19960 citations

Clusters and Critical Behavior in the Ising Model

Jean-Luc Cambier

Jan 1, 19850 citations

New Cluster Method for the Ising Model

Hans Gerd Evertz, H. M. Erkinger, Wolfgang von der Linden

Springer proceedings in physicsJan 1, 20023 citations

TWO-PARTICLE CLUSTER APPROXIMATION FOR ISING TYPE MODEL WITH ARBITRARY VALUE OF SPIN. CORRELATION FUNCTIONS OF BLUME-EMERY-GRIFFITHS MODEL

Sorokov, Levitskii, O. R. Baran

Introduction Among pseudospin systems studied theoretically, a great attention is paid to Ising-type models, that is, to systems with the Hamiltonian containing only z-component of pseudospin. That is so due to relative simplicity with which approximate calculations for these models can be carried out and tested and possibility of their application to a wide class of real objects. Thus, the Blume-Emery-Griffiths model (BEG) corresponding to the Isingtype model with j = 2 (hereafter S z = \\Gammaj; \\Gammaj +2; : : : ; j \\Gamma 2; j) was proposed for the investigation of phase transitions (PT) in He 3 \\Gamma He 4 mixture [1]. A general form of the Ising-type model with j = 2 contains extra terms, as compared to the BEG model, like S z i (S z j<Introduction Among pseudospin systems studied theoretically, a great attention is paid to Ising-type models, that is, to systems with the Hamiltonian containing only z-component of pseudospin. That is so due to relative simplicity with which approximate calculations for these models can be carried out and tested and possibility of their application to a wide class of real objects. Thus, the Blume-Emery-Griffiths model (BEG) corresponding to the Isingtype model with j = 2 (hereafter S z = \\Gammaj; \\Gammaj +2; : : : ; j \\Gamma 2; j) was proposed for the investigation of phase transitions (PT) in He 3 \\Gamma He 4 mixture [1]. A general form of the Ising-type model with j = 2 contains extra terms, as compared to the BEG model, like S z i (S z j<

Condensed Matter PhysicsJan 1, 19974 citations

S^z=\pm1

) the expressions for pair and ternary correlation functions within two-particle approximation in

\set{q}

-space are obtained for the hypercubic Bravais lattices. In the 1D case the exact expressions for them in the site space is obtained as well. On the basis of the Glauber equation within two-particle cluster approximation the longitudinal dynamical susceptibility

χ(\set{q},E)

is found. In the 1D case and in the absence of external field the expression for

χ(\set{q},E)

is exact. For the Emery-Blume-Griffiths model (

S^z=-2,0,2

) within two-particle approximation the pair correlation functions are calculated. The four-particle cluster approximation is used for calculation of static susceptibility

χ(\set{q})

KD_2PO_4

ferroelectrics.