arXiv:cond-mat/0207200

The Magnetization by the Finite Energy Constant Magnetic Field in the Two - Dimentional Ising Model

Yury M. Zinoviev

Published Jul 8, 2002• 0 citations

Abstract

We suggest the new definition of the magnetization. For the two - dimensional Ising model with the free boundary conditions we calculate this magnetization.

DOI: 10.48550/arxiv.cond-mat/0207200

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arXiv:cond-mat/0207200

The Magnetization by the Finite Energy Constant Magnetic Field in the Two - Dimentional Ising Model

Yury M. Zinoviev

Published Jul 8, 2002• 0 citations

arXiv HTML PDF

Abstract

We suggest the new definition of the magnetization. For the two - dimensional Ising model with the free boundary conditions we calculate this magnetization.

DOI: 10.48550/arxiv.cond-mat/0207200

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According to finite-size scaling theory, the correlation length in an Ising strip with infinite length and a width of L lattice constants has the form ${\ensuremath{\xi}}_{L}$(T)=Lf(c(T- ${T}_{c}$ )L) in the scaling regime L\ensuremath{\gg}1,\ensuremath{\Vert}T- ${T}_{c}$ \ensuremath{\Vert}/ ${T}_{c}$ \ensuremath{\ll}1. Here f(x) is a universal scaling function, which does, however, depend on the boundary conditions at the edges of the strip. Utilizing the correspondence between the two-dimensional Ising model and the one-dimensional quantum Ising model in a transverse field, we calculate the explicit form of the function f(x) for spin-spin and energy-energy correlations in strips with periodic, free, fixed, and mixed free-fixed boundary conditions.According to finite-size scaling theory, the correlation length in an Ising strip with infinite length and a width of L lattice constants has the form ${\ensuremath{\xi}}_{L}$(T)=Lf(c(T-${T}_{c}$)L) in the scaling regime L\ensuremath{\gg}1,\ensuremath{\Vert}T-${T}_{c}$\ensuremath{\Vert}/${T}_{c}$\ensuremath{\ll}1. Here f(x) is a universal scaling function, which does, however, depend on the boundary conditions at the edges of the strip. Utilizing the correspondence between the two-dimensional Ising model and the one-dimensional quantum Ising model in a transverse field, we calculate the explicit form of the function f(x) for spin-spin and energy-energy correlations in strips with periodic, free, fixed, and mixed free-fixed boundary conditions.

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R. Z. Bariev, O.A. Malov, N.A. Barieva

Physica A Statistical Mechanics and its ApplicationsNov 1, 19901 citation

According to finite-size scaling theory, the correlation length in an Ising strip with infinite length and a width of L lattice constants has the form ${\ensuremath{\xi}}_{L}$(T)=Lf(c(T-

{T}_{c}

)L) in the scaling regime L\ensuremath{\gg}1,\ensuremath{\Vert}T-

{T}_{c}

\ensuremath{\Vert}/

{T}_{c}

\ensuremath{\ll}1. Here f(x) is a universal scaling function, which does, however, depend on the boundary conditions at the edges of the strip. Utilizing the correspondence between the two-dimensional Ising model and the one-dimensional quantum Ising model in a transverse field, we calculate the explicit form of the function f(x) for spin-spin and energy-energy correlations in strips with periodic, free, fixed, and mixed free-fixed boundary conditions.