The susceptibility of the restricted-dimensional (one- or two-dimensional-like) Ising model is analyzed by means of the high temperature series expansion. The exchange interaction in a chain (or plane), and inter chains (or planes) are J and λ J , respectively. The first eight terms in the susceptibility series are explicitly obtained. The critical temperature T c and the critical exponent γ are obtained as a function of λ. It is found that the susceptibility shows restricted-dimensional behavior at high temperature ( T ≫ T c ), and shows three-dimensional behavior in the very vicinity of the critical temperature ( $T{\gtrsim}T_{\text{c}}$ ) for small λ.The susceptibility of the restricted-dimensional (one- or two-dimensional-like) Ising model is analyzed by means of the high temperature series expansion. The exchange interaction in a chain (or plane), and inter chains (or planes) are J and λ J , respectively. The first eight terms in the susceptibility series are explicitly obtained. The critical temperature T c and the critical exponent γ are obtained as a function of λ. It is found that the susceptibility shows restricted-dimensional behavior at high temperature ( T ≫ T c ), and shows three-dimensional behavior in the very vicinity of the critical temperature ($T{\gtrsim}T_{\text{c}}$) for small λ.

Journal of the Physical Society of JapanOct 1, 19721 citation

Susceptibility of the Ising Model of an Antiferromagnet

M F Sykes, Michael Ellis Fisher

Physical Review LettersNov 1, 195847 citations

Susceptibility scaling functions for ferromagnetic Ising films

T. Weston Capehart, Michael Ellis Fisher

The susceptibility of simple-cubic-lattice ferromagnetic Ising films of $n$ two-dimensional lattice layers is studied by extrapolation of high-temperature series expansions (to eleventh and twelfth orders) for $n=3,4,\dots{},14$ layers with periodic boundary conditions, and $n=3,4,\dots{},10$ layers with free-surface conditions. The corresponding surface susceptibility series for sc, bcc, and fcc lattices are analyzed in the light of universality hypotheses. On the basis of finite-size scaling theory explicit scaling functions are constructed describing the crossover from two-dimensional to three-dimensional critical behavior in terms of the ratio $\frac{n}{\ensuremath{\xi}(T)}$, where $\ensuremath{\xi}\ensuremath{\sim}\ensuremath{\Delta}{T}^{\ensuremath{-}\ensuremath{\nu}}$ is the bulk correlation length.The susceptibility of simple-cubic-lattice ferromagnetic Ising films of $n$ two-dimensional lattice layers is studied by extrapolation of high-temperature series expansions (to eleventh and twelfth orders) for $n=3,4,\dots{},14$ layers with periodic boundary conditions, and $n=3,4,\dots{},10$ layers with free-surface conditions. The corresponding surface susceptibility series for sc, bcc, and fcc lattices are analyzed in the light of universality hypotheses. On the basis of finite-size scaling theory explicit scaling functions are constructed describing the crossover from two-dimensional to three-dimensional critical behavior in terms of the ratio $\frac{n}{\ensuremath{\xi}(T)}$, where $\ensuremath{\xi}\ensuremath{\sim}\ensuremath{\Delta}{T}^{\ensuremath{-}\ensuremath{\nu}}$ is the bulk correlation length.

Physical review. B, Solid stateJun 1, 1976123 citations

T{\gtrsim}T_{\text{c}}

) for small λ.

The susceptibility of simple-cubic-lattice ferromagnetic Ising films of

n

two-dimensional lattice layers is studied by extrapolation of high-temperature series expansions (to eleventh and twelfth orders) for

n=3,4,\dots{},14

layers with periodic boundary conditions, and

n=3,4,\dots{},10

layers with free-surface conditions. The corresponding surface susceptibility series for sc, bcc, and fcc lattices are analyzed in the light of universality hypotheses. On the basis of finite-size scaling theory explicit scaling functions are constructed describing the crossover from two-dimensional to three-dimensional critical behavior in terms of the ratio $\frac{n}{\ensuremath{\xi}(T)}$, where $\ensuremath{\xi}\ensuremath{\sim}\ensuremath{\Delta}{T}^{\ensuremath{-}\ensuremath{\nu}}$ is the bulk correlation length.