147 research outputs found
Bethe roots and refined enumeration of alternating-sign matrices
The properties of the most probable ground state candidate for the XXZ spin
chain with the anisotropy parameter equal to -1/2 and an odd number of sites is
considered. Some linear combinations of the components of the considered state,
divided by the maximal component, coincide with the elementary symmetric
polynomials in the corresponding Bethe roots. It is proved that those
polynomials are equal to the numbers providing the refined enumeration of the
alternating-sign matrices of order M+1 divided by the total number of the
alternating-sign matrices of order M, for the chain of length 2M+1.Comment: LaTeX 2e, 12 pages, minor corrections, references adde
Exact and simple results for the XYZ and strongly interacting fermion chains
We conjecture exact and simple formulas for physical quantities in two
quantum chains. A classic result of this type is Onsager, Kaufman and Yang's
formula for the spontaneous magnetization in the Ising model, subsequently
generalized to the chiral Potts models. We conjecture that analogous results
occur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, and
in a related fermion chain with strong interactions and supersymmetry. We find
exact formulas for the magnetization and gap in the former, and the staggered
density in the latter, by exploiting the fact that certain quantities are
independent of finite-size effects
Ground State of the Quantum Symmetric Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to .Comment: 6 page
The development of blockchain technology in Russia : outlook and trends
Purpose: The article addresses the issue of new scientific decisions shaping with respect to the study of problems, current trends and perspectives of blockchain technology usage in the Russian Federation. Design/methodology/approach: To achieve the objectives of this study the increasing interest to blockchain technology in Russia was discussed. Findings: The article determined main problems in blockchain technology which includes gaps in legislative regulation; the existence of a considerable number of projects that are undergoing the development stage and that have not proved own economic feasibility yet; incomplete understanding of the blockchain spheresâ implementation by state officials, society and business representatives as well as expected outcomes according to the amount and time of their receiving; disputes on cryptocurrencies turnover in the countryâs territory and their influence in the national economy. Practical implications: The study has demonstrated the interest growth mainly by businesses to the usage of blockchain technology in order to improve own competitiveness and to obtain additional benefits, including the form of their profits. Originality/value: The research has also determined the area of further key studies in blockchain technology usage in Russia and the world.peer-reviewe
A new representation for the partition function of the six vertex model with domain wall boundaries
We obtain a new representation for the partition function of the six vertex
model with domain wall boundaries using a functional equation recently derived
by the author. This new representation is given in terms of a sum over the
permutation group where the partial homogeneous limit can be taken trivially.
We also show by construction that this partition function satisfies a linear
partial differential equation.Comment: 14 pages, v2: added references, accepted for publication in J. Stat.
Mec
The role of orthogonal polynomials in the six-vertex model and its combinatorial applications
The Hankel determinant representations for the partition function and
boundary correlation functions of the six-vertex model with domain wall
boundary conditions are investigated by the methods of orthogonal polynomial
theory. For specific values of the parameters of the model, corresponding to
1-, 2- and 3-enumerations of Alternating Sign Matrices (ASMs), these
polynomials specialize to classical ones (Continuous Hahn, Meixner-Pollaczek,
and Continuous Dual Hahn, respectively). As a consequence, a unified and
simplified treatment of ASMs enumerations turns out to be possible, leading
also to some new results such as the refined 3-enumerations of ASMs.
Furthermore, the use of orthogonal polynomials allows us to express, for
generic values of the parameters of the model, the partition function of the
(partially) inhomogeneous model in terms of the one-point boundary correlation
functions of the homogeneous one.Comment: Talk presented by F.C. at the Short Program of the Centre de
Recherches Mathematiques: Random Matrices, Random Processes and Integrable
Systems, Montreal, June 20 - July 8, 200
- âŠ