arXiv subjects

Martin S. Kochman'ski

Publications and source records attributed to Martin S. Kochman'ski.

4 recordsLinked to original sources

arXiv1998

On the two- and three-dimensional Lenz-Ising-Onsager problem in presence of magnetic field

In this paper a new approach to solving the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the twodimensional and threedimensional Ising model with interaction of the nearest neighbors are derived. The representations of free energy being expressed by multidimensional integrals of Gauss type with the appropriate dimensionality are shown. Possibility of calculating the integrals and the critical indices on the base of the derived representations for free energy is investigated.

cond-mat.stat-mech↗

arXiv1998

Jordan-Wigner transformations and their generalizations for multidimensional systems

In the paper nonlinear transformations of the Jordan-Wigner (JW) type are introduced in the form different from the ones known previously, for the purpose of expressing multi-index Pauli operators in terms of multi-index Fermi creation and annihilation operators. These JW transformations in the general case being a subject of a rather complicated algebra of transposition relations between various sets of Fermi creation and annihilation operators, depending on the common multiindex of the latter, is shown. As an example, the two- and three- dimensional transformations of the JW type are investigated, their properties and possible applications in analysis of a couple of lattice models of statistical mechanics and also an example of application of these transformations to problems of self-avoiding walks in graph theory, are discussed. The relation of the obtained transformations to the previously known transformations of the JW type for higher dimensions is shown.

cond-mat.stat-mech↗

arXiv1997

Low-temperature asymptotics of free energy of 3D Ising model in an external magnetic field

The paper presents new method for calculating the low-temperature asymptotics of free energy of the 3D Ising model in external magnetic field $(H\neq 0)$. The results obtained are valid in the wide range of temperature and magnetic field values fulfilling the condition: $[1-\tanh(h/2)]\simε,$ for $ε\ll 1$, where $h=βH$, $β$ - the inverse temperature and $H$ - external magnetic field. For this purpose the method of transfer-matrix, and generalized Jordan-Wigner transformations, in the form introduced by the author in $\cite{mkoch95}$, are applied.

cond-mat.stat-mech↗

arXiv1997

Lenz-Ising-Onsager problem in an external field as a soluble problem of many fermions

In this paper a new approach to solving the 2D and 3D Ising models in external magnetic field $H\neq0$ is developed. The general formalism for the approach to the problem is presented on the example of the 2D Ising model in the external magnetic field. The paper presents a new method obtaining the Onsager solution and computations of asymptotic forms of low-temperature free energy for the 2D Ising model in the external magnetic field $(H)$. The free energy in the limiting case of the magnetic field tending to zero $(H\to 0, N,M\to\infty)$ at arbitrary temperature is also considered $(T\neq 0)$.

cond-mat.stat-mech↗