13 research outputs found
-matrix representation of the finite temperature propagator in -QFT
The two-point Green function of the massive scalar -quantum field
theory with interaction at finite temperature is evaluated up
to the 2nd order of perturbation theory. The averaging on the vacuum
fluctuations is separated from the averaging on the thermal fluctuations
explicitly. As a result, the temperature dependent part of the propagator is
expressed through the scattering amplitudes. The obtained expression is
generalized for higher orders of perturbation theory.Comment: 9 page
On Duality of Two-dimensional Ising Model on Finite Lattice
It is shown that the partition function of the 2d Ising model on the dual
finite lattice with periodical boundary conditions is expressed through some
specific combination of the partition functions of the model on the torus with
corresponding boundary conditions. The generalization of the duality relations
for the nonhomogeneous case is given. These relations are proved for the
weakly-nonhomogeneous distribution of the coupling constants for the finite
lattice of arbitrary sizes. Using the duality relations for the nonhomogeneous
Ising model, we obtain the duality relations for the two-point correlation
function on the torus, the 2d Ising model with magnetic fields applied to the
boundaries and the 2d Ising model with free, fixed and mixed boundary
conditions.Comment: 18 pages, LaTe
Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov -model for N=2
We find a representation of the row-to-row transfer matrix of the
Baxter-Bazhanov-Stroganov -model for N=2 in terms of an integral over
two commuting sets of grassmann variables. Using this representation, we
explicitly calculate transfer matrix eigenvectors and normalize them. It is
also shown how form factors of the model can be expressed in terms of
determinants and inverses of certain Toeplitz matrices.Comment: 23 page
-Deformed Grassmann Field and the Two-dimensional Ising Model
In this paper we construct the exact representation of the Ising partition
function in the form of the -invariant functional integral for the
lattice free -fermion field theory (). It is shown that the
-fermionization allows one to re-express the partition function of the
eight-vertex model in external field through functional integral with
four-fermion interaction. To construct these representations, we define a
lattice -deformed Grassmann bispinor field and extend the Berezin
integration rules to this field. At we obtain the lattice
-fermion field which allows us to fermionize the two-dimensional Ising
model. We show that the Gaussian integral over -Grassmann variables is
expressed through the -deformed Pfaffian which is equal to square root
of the determinant of some matrix at .Comment: 24 pages, LaTeX; minor change
Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes
We develop a finite temperature field theory formalism in any dimension that
has the filling fractions as the basic dynamical variables. The formalism
efficiently decouples zero temperature dynamics from the quantum statistical
sums. The zero temperature `data' is the scattering amplitudes. A saddle point
condition leads to an integral equation which is similar in spirit to the
thermodynamic Bethe ansatz for integrable models, and effectively resums
infinite classes of diagrams. We present both relativistic and non-relativistic
versions
Integral equations and large-time asymptotics for finite-temperature Ising chain correlation functions
This work concerns the dynamical two-point spin correlation functions of the
transverse Ising quantum chain at finite (non-zero) temperature, in the
universal region near the quantum critical point. They are correlation
functions of twist fields in the massive Majorana fermion quantum field theory.
At finite temperature, these are known to satisfy a set of integrable partial
differential equations, including the sinh-Gordon equation. We apply the
classical inverse scattering method to study them, finding that the ``initial
scattering data'' corresponding to the correlation functions are simply related
to the one-particle finite-temperature form factors calculated recently by one
of the authors. The set of linear integral equations (Gelfand-Levitan-Marchenko
equations) associated to the inverse scattering problem then gives, in
principle, the two-point functions at all space and time separations, and all
temperatures. From them, we evaluate the large-time asymptotic expansion ``near
the light cone'', in the region where the difference between the space and time
separations is of the order of the correlation length