4,067 research outputs found
Critical behavior of the spin correlation function in Ashkin-Teller and Baxter models with a line defect
We consider the critical spin-spin correlation function of the Ashkin-Teller
and Baxter models. By using path-integral techniques in the continuum
description of these models in terms of fermion fields, we show that the
correlation decays with distance with the same critical exponent as the Ising
model. The procedure is straightforwardly extended to take into account the
presence of a line defect. Thus we find that in these altered models the
critical index of the magnetic correlation on the defect coincides with the one
of the defective 2D Ising or Bariev's model.Comment: Expanded explanations. Added references. Accepted for publication in
Phys. Rev.
A new integrable two parameter model of strongly correlated electrons in one dimension
A new one-dimensional fermion model depending on two independent interaction
parameters is formulated and solved exactly by the Bethe ansatz method. The
Hamiltonian of the model contains the Hubbard interaction and correlated
hopping as well as pair hopping terms. The density-density and pair
correlations are calculated which manifest superconducting properties in
certain regimes of the phase diagram.Comment: 8 pages, latex, 2 postscript figure
Exact Solution of a Vertex Model with Unlimited Number of States Per Bond
The exact solution is obtained for the eigenvalues and eigenvectors of the
row-to-row transfer matrix of a two-dimensional vertex model with unlimited
number of states per bond. This model is a classical counterpart of a quantum
spin chain with an unlimited value of spin. This quantum chain is studied using
general predictions of conformal field theory. The long-distance behaviour of
some ground-state correlation functions is derived from a finite-size analysis
of the gapless excitations.Comment: 11pages, 6 figure
Integrable model of interacting XX and Fateev-Zamolodchikov chains
We consider the exact solution of a model of correlated particles, which is
presented as a system of interacting XX and Fateev-Zamolodchikov chains. This
model can also be considered as a generalization of the multiband anisotropic
model in the case we restrict the site occupations to at most two
electrons. The exact solution is obtained for the eigenvalues and eigenvectors
using the Bethe-ansatz method.Comment: 10 pages, no figure
Critical behavior at the interface between two systems belonging to different universality classes
We consider the critical behavior at an interface which separates two
semi-infinite subsystems belonging to different universality classes, thus
having different set of critical exponents, but having a common transition
temperature. We solve this problem analytically in the frame of mean-field
theory, which is then generalized using phenomenological scaling
considerations. A large variety of interface critical behavior is obtained
which is checked numerically on the example of two-dimensional q-state Potts
models with q=2 to 4. Weak interface couplings are generally irrelevant,
resulting in the same critical behavior at the interface as for a free surface.
With strong interface couplings, the interface remains ordered at the bulk
transition temperature. More interesting is the intermediate situation, the
special interface transition, when the critical behavior at the interface
involves new critical exponents, which however can be expressed in terms of the
bulk and surface exponents of the two subsystems. We discuss also the smooth or
discontinuous nature of the order parameter profile.Comment: 16 pages, 9 figures, published version, minor changes, some
references adde
Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model
We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov
model is dependent on four spin variables which are the linear combinations of
the spins on the corner sites of the cube and the Wu-Kadanoff duality between
the cube and vertex type tetrahedron equations is obtained explicitly for the
Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by
considering the symmetry property of the weight function, which is
corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type
weight function is parametrized as the dihedral angles between the rapidity
planes connected with the cube. And we write down the symmetry relations of the
weight functions under the actions of the symmetry group of the cube. The
six angles with a constrained condition, appeared in the tetrahedron equation,
can be regarded as the six spectrums connected with the six spaces in which the
vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29
Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method
Two-dimensional ferromagnetic N-state clock models are studied on a
hyperbolic lattice represented by tessellation of pentagons. The lattice lies
on the hyperbolic plane with a constant negative scalar curvature. We observe
the spontaneous magnetization, the internal energy, and the specific heat at
the center of sufficiently large systems, where the fixed boundary conditions
are imposed, for the cases N>=3 up to N=30. The model with N=3, which is
equivalent to the 3-state Potts model on the hyperbolic lattice, exhibits the
first order phase transition. A mean-field like phase transition of the second
order is observed for the cases N>=4. When N>=5 we observe the Schottky type
specific heat below the transition temperature, where its peak hight at low
temperatures scales as N^{-2}. From these facts we conclude that the phase
transition of classical XY-model deep inside the hyperbolic lattices is not of
the Berezinskii-Kosterlitz-Thouless type.Comment: REVTeX style, 4 pages, 6 figures, submitted to Phys. Rev.
Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions
The aim of this contribution is to give the explicit formulas for the
eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model
(N-state spin model) with fixed-spin boundary conditions. These formulas are
obtained by a limiting procedure from the formulas for the eigenvectors of
periodic BBS model. The latter formulas were derived in the framework of the
Sklyanin's method of separation of variables. In the case of fixed-spin
boundaries the corresponding T-Q Baxter equations for the functions of
separated variables are solved explicitly. As a particular case we obtain the
eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.Comment: 14 pages, paper submitted to Proceedings of the International
Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007
Interpolation between Hubbard and supersymmetric t-J models. Two-parameter integrable models of correlated electrons
Two new one-dimensional fermionic models depending on two independent
parameters are formulated and solved exactly by the Bethe-ansatz method. These
models connect continuously the integrable Hubbard and supersymmetric t-J
models.Comment: 11pages and no figure
The application of the global isomorphism to the surface tension of the liquid-vapor interface of the Lennard-Jones fluids
In this communication we show that the surface tension of the real fluids of
the Lennard-Jones type can be obtained from the surface tension of the lattice
gas (Ising model) on the basis of the global isomorphism approach developed
earlier for the bulk properties.Comment: 8 pages, 6 figure
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