The free energy of the Kac-Baker model for spin systems with free surfaces is exactly calculated. The critical temperature is obtained and its shift index $\ensuremath{\lambda}$ evaluated. It is shown that for Ising-like interaction $\ensuremath{\lambda}=\frac{1}{\ensuremath{\nu}}$ ($\ensuremath{\nu}$ is the correlation-length critical index of the bulk), while for the spherical model with overall constraint $\ensuremath{\lambda}=1$; it is argued that the value $\ensuremath{\lambda}=1$ is determined by the imposed constraint. As a byproduct an exact analytical expression for the magnetization of an open Ising chain with random fields is obtained.The free energy of the Kac-Baker model for spin systems with free surfaces is exactly calculated. The critical temperature is obtained and its shift index $\ensuremath{\lambda}$ evaluated. It is shown that for Ising-like interaction $\ensuremath{\lambda}=\frac{1}{\ensuremath{\nu}}$ ($\ensuremath{\nu}$ is the correlation-length critical index of the bulk), while for the spherical model with overall constraint $\ensuremath{\lambda}=1$; it is argued that the value $\ensuremath{\lambda}=1$ is determined by the imposed constraint. As a byproduct an exact analytical expression for the magnetization of an open Ising chain with random fields is obtained.

Physical review. B, Solid stateDec 1, 19761 citation

Critical aspects of the random-field Ising model

Nikolaos G. Fytas, Panagiotis E. Theodorakis, Ioannis Georgiou +1 more

The European Physical Journal BJun 1, 201311 citations

Ground-state numerical study of the three-dimensional random-field Ising model

Ilija Dukovski, Jonathan L. Machta

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to ${60}^{3}.$ For each realization of the normalized random fields, the strength of the random field, $\ensuremath{\Delta}$ and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the $H\ensuremath{-}\ensuremath{\Delta}$ plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to ${60}^{3}.$ For each realization of the normalized random fields, the strength of the random field, $\ensuremath{\Delta}$ and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the $H\ensuremath{-}\ensuremath{\Delta}$ plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.

arXiv:cond-mat/0207438Physical review. B, Condensed matterJan 21, 200340 citations

The random field method for the Ising model

S. I. Kubarev

Physics Letters AAug 1, 19772 citations

The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to

{60}^{3}.

For each realization of the normalized random fields, the strength of the random field, $\ensuremath{\Delta}$ and a uniform external, H is adjusted to find the finite-size critical point. The finite-size critical point is identified as the point in the $H\ensuremath{-}\ensuremath{\Delta}$ plane where three degenerate ground states have the largest discontinuities in the magnetization. The discontinuities in the magnetization and bond energy between these ground states are used to calculate the magnetization and specific heat critical exponents and both exponents are found to be near zero.