Related papers: Noncompact sigma-models: Large N expansion and the…
The action of the 2d O(3) non-linear sigma model on the lattice in a bath of particles, when expressed in terms of standard O(3) degrees of freedom, is complex. A reformulation of the model in terms of new variables that makes the action…
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems,…
Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in…
We study the $O(N)$ non-linear $\sigma$ model on three-dimensional manifolds of constant curvature by means of the large $N$ expansion at the critical point. We examine saddle point equations imposing anti-periodic boundary condition in…
We show that the noncommutativity of space-time destroys the renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the…
The computation of the step scaling function for the finite size mass-gap in the O(N) sigma model at large N is reviewed. Practically exact nonperturbative results become available for both finite and vanishing lattice spacing. We use them…
We argue that the two-dimensional $O(N)$-invariant lattice $\sigma$-model with mixed isovector/isotensor action has a one-parameter family of nontrivial continuum limits, only one of which is the continuum $\sigma$-model constructed by…
Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we…
This is an edited version of an unpublished 1979 EFI (U. Chicago) preprint: "The U(N) lattice gauge theory in 2-dimensions can be considered as the statistical mechanics of a Coulomb gas on a circle in a constant electric field. The large N…
We show how non-commutativity arises from commutativity in the double sigma model. We demonstrate that this model is intrinsically non-commutative by calculating the propagators. In the simplest phase configuration, there are two dual…
Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…
We calculate finite temperature effects on a correlation function in the two dimensional supersymmetric nonlinear O(3) sigma model. The correlation function violates chiral symmetry and at zero temperature it has been shown to be a…
The circular $\beta$ ensemble for $\beta =1,2$ and 4 corresponds to circular orthogonal, unitary and symplectic ensemble respectively as introduced by Dyson. The statistical state of the eigenvalues is then a determinantal point process…
We examine the strong coupling limit of both compact and non compact QED on a lattice with staggered fermions. We show that every SU(N) antiferromagnet with spins in a particular fundamental representation of the SU(N) Lie Algebra and with…
The critical behavior of two-dimensional ${\rm O}(N)$ $\sigma$ models with $N\leq 2$ on the square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green's…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…
We review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…
The $O(3)$ nonlinear $\sigma$ model is studied in the disordered phase, using the techniques of the effective action and finite temperature field theory. The nonlinear constraint is implemented through a Lagrange multiplier. The finite…
In this paper we investigate some particular spin lattice (a higher dimensional generalization of a spin chain) related to Zamolodchikov model, in the limit when both sizes of the lattice tend to infinity. An infinite set of bilinear…
We have considered the corrections to the finite-size-scaling functions for a general class of $O(N)$ $\sigma$-models with two-spin interactions in two dimensions for $N=\infty$. We have computed the leading corrections finding that they…