Classical solutions of two-dimensional Grassmannian models

We present classical solutions of two-dimensional Euclidean Grassmannian σ models (harmonic maps) and discuss some of their properties.     

Some properties of classical solutions in Grassmannian sigma models

We investigate the construction of a large class of classical solutions to the nonabelian Grassmannian sigma models in two Euclidean space-time dimensions and also discuss the problem of uniqueness. Some spectral types of solutions have interesting features when represented in the framework of the Riemann-Hilbert problem.Research supported by the Swiss National Science Foundation.     

Stability properties of classical solutions to non-linear σ models

We show that the classical solutions of two-dimensional euclidean O(2p + 1) non-linear σ models given in terms of spherical harmonics are unstable under small perturbations for p ? 2. The negative and zero energy fluctuation modes are displayed.     

Tensor renormalization group approach to two-dimensional classical lattice models

We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.     

On the integrability of classical spinor models in two-dimensional space-time

Well known classical spinor relativistic-invariant two-dimensional field theory models, including the Gross-Neveu, Vaks-Larkin-Nambu-Jona-Lasinio and some other models, are shown to be integrable by means of the inverse scattering problem method. These models are shown to be naturally connected with the principal chiral fields on the symplectic, unitary and orthogonal Lie groups. The respective technique for construction of the soliton-like solutions is developed.     

Analytic instanton solutions in two-dimensional field models

Two-dimensional scalar field models with nontrivial potential determined in bounded spatial regions are considered. Exact analytic instanton solutions for these models and soliton solutions for similar three-dimensional systems are obtained.     

Classical solutions in Grassmannian σ-models

We study the generalisation of the CP ⁿ⁻¹ model in two-dimensional Euclidean space-time to Grassmannian σ-models having a non-Abelian gauge group. Some classes of classical solutions are displayed. It appears that the general solutions involve complicated constraints.     

Further properties of classical solutions in grassmannian σ models

We calculate the action and the topological charge of classical solutions in two-dimensional euclidean grassmannian σ models (for both generic and special solutions). We show that all the above non-instanton or non-anti-instanton solutions are unstable. We also find solutions of the Dirac equation describing fermions in the background of these grassmannian fields, and we exhibit relations between these fermionic solutions and those of the associated Hilbert-Riemann problem.     

Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super-Grassmannian manifolds, that is, coset supermanifolds G(m,p|n,q)≅U(m|n)/[U(p|q)⊗U(m−p|n−q)]$G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for 0?p?m$0?p?m$, 0?q?n$0?q?n$ and 1?p+q$1?p+q$. The projective superspace CPm−1|n${\mathbf{CP}}^{m-1|n}$ is a special case of p=1$p=1$, q=0$q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm–Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super-case published more than twenty years ago by one of the present authors.     

Bäcklund transformations and soliton-type solutions for σ models with values in real Grassmannian spaces

A Bäcklund transformation for the two-dimensional σ model with values in oriented real Grassmannian spaces is constructed using the known Bäcklund transformation for the SO(n) principal models. The construction provides a natural way to linearize the differential system of the Bäcklund transformation. In the case of the S ⁿ≈SO(n+1/SOn) model, the Backlund transformation reduces to that of Pohlmeyer. The one-soliton solution for S ²～SO(3)/SO(2) is obtained analytically and plots of one-soliton and two-soliton solutions are displayed.     

A Monte Carlo study of two-dimensional classical easy-plane Heisenberg models with symmetry-breaking

Monte Carlo studies of thermodynamic functions for quasi-2-dimensional classical ferromagnets are reported. Easy-plane Heisenberg models with Ising and 6-fold symmetry breaking fields in the easy-plane are emphasized as models of Rb₂CrCl₄ and CoCl₂-intercalated graphite.     

Stiefel-Skyrme-Higgs models,their classical static solutions and Yang-Mills-Higgs monopoles

A new series of models is introduced by adding Higgs fields to the earlier proposed Euclidean four-dimensional Skyrme-like models with Yang-Mills composite fields constructed from Stiefel manifold-valued fields. The classical static versions of these models are discussed. The connection with the monopole solutions of the Yang-Mills-Higgs models in the Prasad-Sommerfield limit is pointed out and the BPS monopole is reobtained as an example. On leave of absence from the Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria.     

Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models

It is well known that instantons are classical topological solutions existing in the context of quantum field theories that lie behind the standard model of particles. To provide a better understanding for the dynamical nature of spinor-type instanton solutions, conformal invariant pure spinor fermionic models that admit particle-like solutions for the derived classical field equations are studied in this work under cosine wave forcing. For this purpose, the effects of external periodic forcing on two systems that have different dimensions and quantum spinor numbers and have been obtained under the use of Heisenberg ansatz are investigated by constructing their Poincaré sections in phase space. As a result, bifurcations and chaos are observed depending on the excitation amplitude of the external forcing in both pure spinor fermionic models.     

Supersymmetry and classical solutions

We obtain classical solutions to the field equations of the massless supersymmetric Wess-Zumino model and to the field equations of the interacting SU(2) gauge supermultiplet. This is done by applying finite supersymmetry transformations to the known solutions of the scalar field equation with ?⁴ interaction and the Yang-Mills field equations. The relevance of supersymmetry to the solution of classical field equations involving anticommuting fermion fields is discussed.     

Mass relations for two-dimensional classical configurations

Using the two-dimensional -nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold.     

Density-functional approach to two-dimensional classical fluids

The density-functional (DF) method is combined with the smoothed-density approximation to calculate the fluid structure in two-dimensional (2D) hard-disc (HD) systems. Density-dependent weighting functions in the DF method proposed by Tarazona for three-dimensional fluids have been applied to 2D systems for the calculation of the radial distribution function of HD fluids and the determination of the static structure of 2D HD fluids around the central hard triatomic molecule. The results compare reasonably well with Monte Carlo data. The radial distribution of a 2D Lennard-Jones fluid has also been calculated and shown to be in satisfactory agreement with Monte Carlo data except for the high-density fluid.