Saddle-points in the twisted reduced chiral model

It is shown that the abnormal behaviour found in numerical simulations of twisted reduced SU(N→∞) chiral model in two dimensions results from fluctuations around a non-trivial extremum of the action. The possible rôle of such saddle-points in the crossover to the strong coupling regime is discussed.     

Twisted reduced chiral model

The idea of twisted reduction of space-time degrees of freedom recently proposed by the present authors is applied to the matrix chiral model. The equivalence of our reduced model and the usual chiral model is established by comparing the Schwinger-Dyson equations and weak coupling expansions and by performing the Monte Carlo simulation.     

Zero-curvature formalism of supersymmetric principal chiral model

We investigate the one-parameter family of transformations on superfields of the super principal chiral model and obtain different zero-curvature representations of the model. The parametric transformation is related to the super Riccati equations and an infinite set of local and non-local conservation laws is derived. A Lax representation of the model is presented which gives rise to a superspace monodromy operator.Received: 2 July 2004, Revised: 13 October 2004, Published online: 7 December 2004     

Boundary scattering in the principal chiral model

An introduction to our recent work (hep-th/0104212) on the (G ×G-invariant) principal chiral model with boundary is presented. We found that both classically integrable boundary conditions and quantum boundary is presentedS-matrices were classified by the symmetric spacesG/H. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

Hamiltonian for the twisted reduced model of large-N QCD

We propose a Hamiltonian for the reduced model with twist of theSU(N→∞) lattice gauge theory. Also we discuss how information as the mass gap, say, might survive under reduction and consider the euclidean Schwinger-Dyson equations for multiloop expectation values.     

On the connection between the principal chiral model and the multiflavour chiral Gross-Neveu model

The infinite flavour limit of the multiflavour chiral Gross-Neveu (MCGN) partition function is shown to be equal to the principal chiral σ-model (PCM) partition function where in addition one integrates over twisted boundary conditions. This last interpretation restricts the space of states to the left (or right) singlet sector. In the course of this derivation, a rigorous paramagnetic inequality for the Dirac determinant is proved. The critical (conformal invariant) points of the MCGN are investigated in connection with critical WZW σ-models.     

On algebraic structures in supersymmetric principal chiral model

Using the Poisson current algebra of the supersymmetric principal chiral model, we develop the algebraic canonical structure of the model by evaluating the fundamental Poisson bracket of the Lax matrices that fits into the r–s matrix formalism of non-ultralocal integrable models. The fundamental Poisson bracket has been used to compute the Poisson bracket algebra of the monodromy matrix that gives the conserved quantities in involution. PACS 11.30.Pb; 02.30.Ik     

The chiral Potts models revisited

We review some exact results obtained so far in the chiral Potts models and translate these results into language more transparent to physicists, so that experts in Monte Carlo calculations, high- and low-temperature expansions, and various other methods can use them. We pay special attention to the interfacial tension _r between thek state and thek-r state. By examining the ground states, it is seen that the integrable line ends at a superwetting point, on which the relation _r =r ₁ is satisfied, so that it is energetically neutral to have one interface or more. We present also some partial results on the meaning of the integrable line for low temperatures, where it lives in the nonwet regime. We make Baxter's exact results more explicit for the symmetric case. By performing a Bethe Ansatz calculation with open boundary conditions we confirm a dilogarithm identity for the low-temperature expansion which may be new. We propose a new model for numerical studies. This model has only two variables and exhibits commensurate and incommensurate phase transitions and wetting transitions near zero temperature. It appears to be not integrable, except at one point, and at each temperature there is a point where it is almost identical with the integrable chiral Potts model.     

Boson-Fermion equivalence in a two-dimensional anomalous chiral model

A current algebraic approach is taken to realise the two-dimensional chiral model having anomaly analogous to that of Wess and Zumino. The conserved currents are shown to be a combination of bosonic and fermionic ones. The equations of motion of the fermions are realised through its commutation algebra with the Sugawara-like energy-momentum tensor. Quantisation of the anomaly parameter is shown to be a consequence of consistent statistics.     

P-odd one-meson exchanges revisited: a non-linear chiral model approach

Coupling constants of theP-odd interaction of nucleon with the π-, ρ-, ω-mesons are calculated in the non-linear chiral model. The hierarchy of these constants governed by small parameters sin² θ _w and 1/N _c is established. According to this hierarchy the ratio of the weak πNN and ρNN coupling constants is small, being ?sin² θ _w /N _c . The absolute values of all considered constants prove to be essentially larger than those in theSU(6) _W model, thus pointing that theP-odd effects due to the overlap of the nucleons' wave functions are of importance.     

From chiral to two-dimensional Wess-Zumino-Novikov-Witten model via quantum gauge group

We study the canonical quantization of the SU(n) WZNW model. Decoupling the chiral dynamics requires an extended state space including left and right monodromies as independent variables. In the simplest (n = 2) case we explicitly show that the zero modes of the monodromy extended SU(2) WZNW model give rise to a quantum group gauge theory in a finite-dimensional Fock space. We define the subspace of U_q(sl(2)) ⊗ U_q(sl(2))-invariant vectors on which the monodromy invariance is also restored and construct the physical space applying a generalized cohomology condition.     

Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited

We investigate the collapse transition of lattice trees with nearest neighbor attraction in two and three dimensions. Two methods are used: (1) A stochastic optimization process of the Robbins-Monro type, which is designed solely to locate the maximum value of the specific heat; and (2) umbrella sampling, which is designed to sample data over a wide temperature range, as well as to combat the quasiergodicity of Metropolis algorithms in the collapsed phase. We find good evidence that the transition is second order with a divergent specific heat, and that the divergence of the specific heat coincides with the metric collapse.     

Emerging properties of two-dimensional twisted bilayer materials

Recent studies in van der Waals coupled two-dimensional(2D) bilayer materials have demonstrated a new freedom for material engineering by the formation of moiré pattern. By tuning the twist angle between two layers, one can modulate their electronic band structures and therefore the associated electrical transport and optical properties, which are distinct from the original ones of each individual layer. These new properties excite great passion in the exploration of new quantum states and possible applications of 2D bilayers. In this article, we will mainly review the prevailing fabrication methods and emerging physical properties of twisted bilayer materials and lastly give out a perspective of this topic.     

The effect of chiral density waves on the superconducting phase in the two-dimensional Gross-Neveu model

The phase structure of a 2-dimensional Gross-Neveu model with a difermion channel of interaction is studied in the variables of the temperature and chemical potentials in the limit of a large number of field components N → ∞.     

On a generalization of the hidden symmetry transformations for the principal chiral model

Nonlocal hidden symmetry transformations with a generalized structure and boundary conditions at spatial infinity for the principal chiral model are proposed. Additional restrictions on these transformations following from the requirement for the existence of an infinite set of conserved nonlocal charges are analyzed. The corresponding Lie algebra is more general than the Kac-Moody one.     

Asymptotically free two-dimensional chiral models

The geometrical part of a one-loop counter term of an arbitrary G-invariant chiral theory on the homogeneous space G/H of the Lie group G is calculated. It is shown that the class of asymptotically free theories is wider than the symmetric spaces.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 92–95, July, 1985.     

The Lennard-Jones-Devonshire cell model revisited

The cell theory of Lennard-Jones and Devonshire is re-analysed and it is found that, in addition to the critical point originally reported for the 12-6 potential (and widely quoted in standard textbooks), the model exhibits a further critical point. The latter is shown to be actually a more appropriate candidate for liquid-gas criticality than the original critical point.     

Local conserved charges in principal chiral models

We present a general construction of local, commuting conserved charges, with spins equal to the exponents, modulo the Coxeter number, of the underlying Lie algebra, for principal chiral models based on the classical Lie groups.