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

Quantum Ising Phases and Transitions in Transverse Ising Models

Bikas K. Chakrabarti, Amit Dutta, Parongama Sen

Lecture notes in physics. M, MonographsJan 1, 1996274 citations

Scaling and density of Lee-Yang zeros in the four-dimensional Ising model

Ralph Kenna B, Christian B. Lang

All of the information on the behavior of the four-dimensional Ising model is contained in the distribution and density of its partition function zeros. This model is believed to belong to the same universality class as the ${\mathrm{\ensuremath{\varphi}}}_{4}^{4}$ model which plays a central role in relativistic quantum field theory. Here the scaling behavior of the edge of the distribution of zeros and the asymptotic form for the density of zeros are determined. The finite-size dependency of the density of zeros---or the distance between zeros---at the infinite volume critical point is found using both analytic and numerical approaches. As with a previous analysis of the lowest lying zero, emphasis is laid on the multiplicative logarithmic corrections to mean field scaling behavior which are related to the triviality of the Ising and ${\mathrm{\ensuremath{\varphi}}}^{4}$ models in four dimensions.All of the information on the behavior of the four-dimensional Ising model is contained in the distribution and density of its partition function zeros. This model is believed to belong to the same universality class as the ${\mathrm{\ensuremath{\varphi}}}_{4}^{4}$ model which plays a central role in relativistic quantum field theory. Here the scaling behavior of the edge of the distribution of zeros and the asymptotic form for the density of zeros are determined. The finite-size dependency of the density of zeros---or the distance between zeros---at the infinite volume critical point is found using both analytic and numerical approaches. As with a previous analysis of the lowest lying zero, emphasis is laid on the multiplicative logarithmic corrections to mean field scaling behavior which are related to the triviality of the Ising and ${\mathrm{\ensuremath{\varphi}}}^{4}$ models in four dimensions.

arXiv:hep-lat/9311029Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 199441 citations

Universal Quantum Dynamics of the Transverse-Field Ising Model

Michael Kolodrubetz, Bryan K. Clark, David A. Huse

Bulletin of the American Physical SocietyMar 1, 20120 citations

Duality of the Two-dimensional Ising Model

Giuseppe Mussardo

Abstract In this chapter we will begin our study of the Ising model on the two-dimensional lattice. In two dimensions the model has a phase transition, with critical exponents that have different values from those obtained in the mean field approximation. For this reason, it provides an important example of critical phenomena. As we will see in great detail in this chapter and in the next, among all exactly solved models of statistical mechanics, the two-dimensional Ising model is not only the one that has been most studied but it is also the model that has given a series of deep mathematical and physical results. Many solutions of the model stand out for the ingenious methods used, such as the theory of determinants, combinatorial approaches, Grassmann variables, or elliptic functions. Many results have deeply influenced the understanding of critical phenomena and have strongly stimulated new fields of research. Ideas that have matured within the study of the two-dimensional Ising model, such as the duality between its highand low-temperature phases, have been readily generalized to other systems of statistical mechanics and have also found important and fundamental applications in other important areas such as, for instance, quantum field theory. Equally fundamental is the discovery that in the vicinity of the critical point, the dynamics of the model can be described from the relativistic Dirac equation for Majorana fermions.Abstract In this chapter we will begin our study of the Ising model on the two-dimensional lattice. In two dimensions the model has a phase transition, with critical exponents that have different values from those obtained in the mean field approximation. For this reason, it provides an important example of critical phenomena. As we will see in great detail in this chapter and in the next, among all exactly solved models of statistical mechanics, the two-dimensional Ising model is not only the one that has been most studied but it is also the model that has given a series of deep mathematical and physical results. Many solutions of the model stand out for the ingenious methods used, such as the theory of determinants, combinatorial approaches, Grassmann variables, or elliptic functions. Many results have deeply influenced the understanding of critical phenomena and have strongly stimulated new fields of research. Ideas that have matured within the study of the two-dimensional Ising model, such as the duality between its highand low-temperature phases, have been readily generalized to other systems of statistical mechanics and have also found important and fundamental applications in other important areas such as, for instance, quantum field theory. Equally fundamental is the discovery that in the vicinity of the critical point, the dynamics of the model can be described from the relativistic Dirac equation for Majorana fermions.

Aug 27, 20090 citations

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.