Series expansions are presented for the magnetisation, susceptibility, magnetic field derivatives of the susceptibility and 'specific heat' of the zero-temperature transverse Ising model. Coefficients in these series have been calculated to tenth order in lambda 2 (where lambda is the transverse field) for the linear chain, to eighth order for the square lattice and to seventh order for the triangular lattice. These series yield estimates of the low-temperature critical exponents alpha ', beta ', gamma ' and Delta ' of the two- and three-dimensional Ising models. They provide good evidence for the symmetry of exponents above and below the critical point, e.g. gamma '= gamma .Series expansions are presented for the magnetisation, susceptibility, magnetic field derivatives of the susceptibility and 'specific heat' of the zero-temperature transverse Ising model. Coefficients in these series have been calculated to tenth order in lambda 2 (where lambda is the transverse field) for the linear chain, to eighth order for the square lattice and to seventh order for the triangular lattice. These series yield estimates of the low-temperature critical exponents alpha ', beta ', gamma ' and Delta ' of the two- and three-dimensional Ising models. They provide good evidence for the symmetry of exponents above and below the critical point, e.g. gamma '= gamma .

Journal of Physics A Mathematical and GeneralAug 1, 198150 citations

On the susceptibility of the three dimensional Ising ferromagnet

Dennis C. Rapaport

Physics Letters AJul 1, 19733 citations

A note on the mean size of clusters in the Ising model

M F Sykes, David S. Gaunt

The derivation of series expansions for the mean size of finite clusters in the Ising model is described briefly. From the analysis of low temperature series it is concluded that for a two-dimensional lattice in zero magnetic field the mean size probably diverges at the Ising critical temperature, T c , as (T c -T) - theta , with theta =1.91+or-0.01. It appears therefore that theta < gamma '=1.75 the corresponding Ising susceptibility exponent. For a three-dimensional lattice it is tentatively concluded that the mean size diverges at some temperature T*<T c .The derivation of series expansions for the mean size of finite clusters in the Ising model is described briefly. From the analysis of low temperature series it is concluded that for a two-dimensional lattice in zero magnetic field the mean size probably diverges at the Ising critical temperature, T c , as (T c -T) - theta , with theta =1.91+or-0.01. It appears therefore that theta < gamma '=1.75 the corresponding Ising susceptibility exponent. For a three-dimensional lattice it is tentatively concluded that the mean size diverges at some temperature T*<T c .

Journal of Physics A Mathematical and GeneralDec 1, 197675 citations

On the susceptibility of the one-dimensional Ising chain

E.J. Van Dongen, Hans W. Capel

Physica A Statistical Mechanics and its ApplicationsJan 1, 197611 citations

The dynamic critical exponent of the three-dimensional Ising model

R. Matz, D. L. Hunter, Naeem Jan

Journal of Statistical PhysicsFeb 1, 199434 citations

Three-dimensional Ising models -- Critical Parameters using $ε$ -convergence method

M V Vismaya, M.V. Sangaranarayanan

We demonstrate the applicability of the $ε$ -convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.We demonstrate the applicability of the $ε$-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.

arXiv:2410.15785Oct 21, 20240 citations

We demonstrate the applicability of the

ε

-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high temperature susceptibility series of simple cubic, body-centered cubic, face-centered cubic and diamond lattices, using two different variables for the inverse critical temperature. In the case of simple cubic lattices, the magnetization series was modified to deduce accurate values of the critical temperatures. The alternate variable for dimensionless inverse temperature suggested by Guttmann and Thompson has also been employed for the estimation of the critical parameters.