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

Symmetry Breaking in the Ising Model

Franco Strocchi

Lecture notes in physicsOct 30, 20073 citations

Pairing-induced Bloch oscillations in an interacting Kitaev chain

E. S. Ma, Z. Song

We study the peculiar dynamics of the Kitaev chain induced by nearest-neighbor (NN) interaction. We show that a strong NN interaction suppresses single-particle hopping but enhances pairing, resulting in a Wannier-Stark ladder. Based on the spin-fermion correspondence at the symmetry point, the model maps to a transverse field Ising model on a zigzag lattice, providing a clear physical picture and guiding experimental verification. The Wannier-Stark state corresponds to a localized domain wall between ferromagnetic and antiferromagnetic phases. It exhibits Bloch oscillation even in the absence of a longitudinal field, in contrast to previous works. Numerical simulations of time-dependent observables verify these conclusions. Our findings provide an example demonstrating emergent Stark many-body localization.We study the peculiar dynamics of the Kitaev chain induced by nearest-neighbor (NN) interaction. We show that a strong NN interaction suppresses single-particle hopping but enhances pairing, resulting in a Wannier-Stark ladder. Based on the spin-fermion correspondence at the symmetry point, the model maps to a transverse field Ising model on a zigzag lattice, providing a clear physical picture and guiding experimental verification. The Wannier-Stark state corresponds to a localized domain wall between ferromagnetic and antiferromagnetic phases. It exhibits Bloch oscillation even in the absence of a longitudinal field, in contrast to previous works. Numerical simulations of time-dependent observables verify these conclusions. Our findings provide an example demonstrating emergent Stark many-body localization.

arXiv:2606.22284Jun 21, 20260 citations

Field-induced freezing in the unfrustrated Ising antiferromagnet

Adam Iaizzi

We study instantaneous quenches from infinite temperature to well below T_{c} in the two-dimensional square lattice Ising antiferromagnet in the presence of a longitudinal external magnetic field. Under single-spin-flip Metropolis algorithm Monte Carlo dynamics, this protocol produces a pair of magnetization plateaus that prevent the system from reaching the equilibrium ground state except for some special values of the field. We explain the plateaus in terms of local spin configurations that are stable under the dynamics.We study instantaneous quenches from infinite temperature to well below T_{c} in the two-dimensional square lattice Ising antiferromagnet in the presence of a longitudinal external magnetic field. Under single-spin-flip Metropolis algorithm Monte Carlo dynamics, this protocol produces a pair of magnetization plateaus that prevent the system from reaching the equilibrium ground state except for some special values of the field. We explain the plateaus in terms of local spin configurations that are stable under the dynamics.

arXiv:2001.09268Physical review. ESep 8, 20201 citation

Dynamics of Quantum Ising Systems

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

Lecture notes in physicsDec 12, 20120 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.