Ising Field Research Articles

Non-linear partial difference equations for the two-spin correlation function of the two-dimensional Ising model

Abstract For all temperatures, the two-point function of the two-dimensional Ising model is shown to be expressible in terms of the solution of a non-linear partial difference equation on the lattice. From this difference equation, the known results for the two-point function of the Ising field theory are regained by taking the scaling limit.

Nonlinear Partial Difference Equations for the Two-Dimensional Ising Model

The two-point function of the two-dimensional Ising model at arbitrary temperature is expressed in terms of the solution of a nonlinear partial difference equation. From this difference equation the known results for the two-point function of the Ising field theory may be regained as a special case.

Supersymmetric Ising field theory

Abstract We construct the simplest solvable non-trivial ( S ≠ 1) supersymmetric model: the supersymmetric Ising field theory. The supersymmetric generalization of the duality order/disorder algebra is discussed. Finally we attempt to “double” the model and comment on the connection between this doubled model and the unsolved problem of the supersymmetric sine-Gordon kink structure.

Z2 duality algebra in D = 2 quantum field theory

We show that the relict of the Kramers-Wannier duality of lattice systems in the scaling limit is the dual algebra and its inequivalent representation. For the Z 2 dual algebra of the Ising field theory there are precisely two inequivalent representations corresponding to T≶T c . The T < T c representation contains a Z 2 “spurion” which is the remainder of a topological zero-momentum mode in the scaling limit. Our discussion of duality in the A 4 theory is less rigorous than for the Ising model.

Two-dimensional Ising field theory forT&lt;Tc: Green's-functions strings inn-point functions

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 $T&lt;{T}_{c}$ 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.

Two-dimensional Ising field theory in a magnetic field: Breakup of the cut in the two-point function

We demonstrate that the cut which is present as the leading singularity in the two-point function of the Ising field theory for $Tl{T}_{c}$ and $H=0$ breaks up into a sequence of poles for $H\ensuremath{\ne}0$. Both the positions and the residues of the low-lying poles are calculated.

Two-dimensional Ising field theory forT&lt;Tc: String structure of the three-point function

We use the recently derived expressions for the $n$-point functions of the two-dimensional Ising field theory for $T&lt;{T}_{c}$ 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.

Exchange-split crystal-field levels ofFe2+in FeCO3

Neutron time-of-flight measurements of the low-lying crystal-field excitations have been taken on both a natural single crystal and pure synthetic powder of FeC${\mathrm{O}}_{3}$ above and below the N\'eel temperature (${T}_{N}=38.4$ K). At 4.2 K the principal allowed excitation was measured to be 13.75\ifmmode\pm\else\textpm\fi{}0.10 meV, in good agreement with previous neutron and far-infrared measurements. A second less intense excitation was observed at 19.75\ifmmode\pm\else\textpm\fi{}0.25 meV. Above ${T}_{N}$ a broadened excitation at 11.2 meV was observed, with a small shoulder persisting on the high-energy side. The measured excitation energies and transition probabilities can be adequately described by a single-ion Hamiltonian which includes spin-orbit coupling, trigonal distortion, and an Ising molecular field, taken in the lowest-lying cubic-crystal-field state of ${\mathrm{Fe}}^{2+}$.

Inequalities for Ising models and field theories which obey the Lee-Yang Theorem

A series of inequalities for partition, correlation, and Ursell functions are derived as consequences of the Lee-Yang Theorem. In particular, then-point Schwinger functions ofeven φ4 models are bounded in terms of the 2-point function as strongly as is the case for Gaussian fields; this strengthens recent results of Glimm and Jaffe and shows that renormalizability of the 2-point function by fourth degree counter-terms implies existence of a φ4 field theory with a moment generating function which is entire of exponential order at most two. It is also noted that ifany (even) truncated Schwinger function vanishes identically, the resulting field theory is a generalized free field.