Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Two-dimensional Ising field theory for T

Barry M. McCoy, Tai Tsun Wu

Published Aug 15, 1978• 11 citations

Abstract

We continue our investigation of the large-separation behavior of the $n$-point connected Green's functions of the two-dimensional Ising field theory for $T<{T}_{c}$ by studying the nearly collinear limit for $n\ensuremath{\ge}4$. The results extend the description of the string structure found in the three-point function.

DOI: 10.1103/physrevd.18.1253

Related papers

Two-dimensional Ising field theory for T

Barry M. McCoy, Tai Tsun Wu

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsAug 15, 197817 citations

Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n -Point Functions

Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu

Physical Review LettersApr 11, 1977140 citations

Correlations and structure of interfaces in the Ising model: theory and numerics

Alessio Squarcini, Antonio Tinti

Abstract We consider phase separation on the strip for the two-dimensional Ising model in the near-critical region. Within the framework of field theory, we find exact analytic results for certain two- and three-point correlation functions of the order parameter field. The analytic results for order parameter correlations, energy density profile, subleading corrections and passage probability density of the interface are confirmed by accurate Monte Carlo simulations we performed.

arXiv:2104.06660Journal of Statistical Mechanics Theory and ExperimentAug 1, 202115 citations

Three-point energy density Green function of the Ising quantum field theory for T<T>c

Hong-Kang Zhao, Mo‐Lin Ge, Mu-Lin Yan

Physics Letters AAug 1, 19930 citations

Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. III

Hung Cheng, Tai Tsun Wu

Physical ReviewDec 10, 196791 citations

Correlation functions in the two-dimensional Ising model in a magnetic field at T = Tc

Gesualdo Delfino A, P. Simonetti

arXiv:hep-th/9605065Physics Letters BSep 1, 199667 citations

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Two-dimensional Ising field theory for T

Barry M. McCoy, Tai Tsun Wu

Published Aug 15, 1978• 11 citations

Publisher

Abstract

We continue our investigation of the large-separation behavior of the

n

-point connected Green's functions of the two-dimensional Ising field theory for

T<{T}_{c}

by studying the nearly collinear limit for

n\ensuremath{\ge}4

. The results extend the description of the string structure found in the three-point function.

DOI: 10.1103/physrevd.18.1253

Related papers

Two-dimensional Ising field theory for T

Barry M. McCoy, Tai Tsun Wu

We use the recently derived expressions for the $n$ -point functions of the two-dimensional Ising field theory for $T<{T}_{c}$ to study the three-point function when the separations between the spins is large. We find that the functional form is different depending on whether or not the three spins are collinear. When the three spins are collinear the asymptotic behavior of the connected three-point function is shown to be independent of the location of the middle spin. We interpret these results in terms of a string of correlation.We use the recently derived expressions for the $n$-point functions of the two-dimensional Ising field theory for $T<{T}_{c}$ to study the three-point function when the separations between the spins is large. We find that the functional form is different depending on whether or not the three spins are collinear. When the three spins are collinear the asymptotic behavior of the connected three-point function is shown to be independent of the location of the middle spin. We interpret these results in terms of a string of correlation.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsAug 15, 197817 citations

Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n -Point Functions

Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu

For both $T>{T}_{c}$ and $T<{T}_{c}$ , we report exact expressions for the $n$ -spin correlation function of the two-dimensional Ising model suitable for studying large separations between spins. In particular, the scaling limit of these correlation functions can be shown to exist and yields $n$ -point Schwinger functions of some relativistic quantum field theories.For both $T>{T}_{c}$ and $T<{T}_{c}$, we report exact expressions for the $n$-spin correlation function of the two-dimensional Ising model suitable for studying large separations between spins. In particular, the scaling limit of these correlation functions can be shown to exist and yields $n$-point Schwinger functions of some relativistic quantum field theories.

Physical Review LettersApr 11, 1977140 citations

Correlations and structure of interfaces in the Ising model: theory and numerics

Alessio Squarcini, Antonio Tinti

arXiv:2104.06660Journal of Statistical Mechanics Theory and ExperimentAug 1, 202115 citations

Three-point energy density Green function of the Ising quantum field theory for T<T>c

Hong-Kang Zhao, Mo‐Lin Ge, Mu-Lin Yan

Physics Letters AAug 1, 19930 citations

Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. III

Hung Cheng, Tai Tsun Wu

We study the asymptotic behavior, for large separations, of the spin-spin correlation function $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{M,N}〉$ in the two-dimensional Ising model, where the two spins are not necessarily on the same row. Besides the limiting value for infinite separation, which is the square of the spontaneous magnetization, we evaluate the two leading terms in the asymptotic expression in each of the two cases $T<{T}_{c}$ and $T>{T}_{c}$ . It is found that the nearest singularity of the generating function for the correlation is quite simple in the case $T>{T}_{c}$ , but much more complicated for $T<{T}_{c}$ . In an Appendix, we also give exactly in a very simple form the correlation $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{N,N}〉$ for symmetrical Ising lattice at the critical temperature ${T}_{c}$ .We study the asymptotic behavior, for large separations, of the spin-spin correlation function $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{M,N}〉$ in the two-dimensional Ising model, where the two spins are not necessarily on the same row. Besides the limiting value for infinite separation, which is the square of the spontaneous magnetization, we evaluate the two leading terms in the asymptotic expression in each of the two cases $T<{T}_{c}$ and $T>{T}_{c}$. It is found that the nearest singularity of the generating function for the correlation is quite simple in the case $T>{T}_{c}$, but much more complicated for $T<{T}_{c}$. In an Appendix, we also give exactly in a very simple form the correlation $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{N,N}〉$ for symmetrical Ising lattice at the critical temperature ${T}_{c}$.

Physical ReviewDec 10, 196791 citations

Correlation functions in the two-dimensional Ising model in a magnetic field at T = Tc

Gesualdo Delfino A, P. Simonetti

arXiv:hep-th/9605065Physics Letters BSep 1, 199667 citations

We continue our investigation of the large-separation behavior of the

n

-point connected Green's functions of the two-dimensional Ising field theory for

T<{T}_{c}

by studying the nearly collinear limit for

n\ensuremath{\ge}4

. The results extend the description of the string structure found in the three-point function.

We use the recently derived expressions for the

n

-point functions of the two-dimensional Ising field theory for

T<{T}_{c}

to study the three-point function when the separations between the spins is large. We find that the functional form is different depending on whether or not the three spins are collinear. When the three spins are collinear the asymptotic behavior of the connected three-point function is shown to be independent of the location of the middle spin. We interpret these results in terms of a string of correlation.

For both

T>{T}_{c}

and

T<{T}_{c}

, we report exact expressions for the

n

-spin correlation function of the two-dimensional Ising model suitable for studying large separations between spins. In particular, the scaling limit of these correlation functions can be shown to exist and yields

n

-point Schwinger functions of some relativistic quantum field theories.

T<{T}_{c}

and

T>{T}_{c}

. It is found that the nearest singularity of the generating function for the correlation is quite simple in the case

T>{T}_{c}

, but much more complicated for

T<{T}_{c}

. In an Appendix, we also give exactly in a very simple form the correlation $〈{\ensuremath{\sigma}}_{0,0}{\ensuremath{\sigma}}_{N,N}〉$ for symmetrical Ising lattice at the critical temperature

{T}_{c}