Progress of Theoretical Physics

High Temperature Series Expansion of the Susceptibility of the d-Dimensional Random Ising Model

Shigeru Okamoto, T. Oguchi, Yohtaro Ueno

Published Feb 1, 1982• 2 citations

Abstract

The critical temperatures of the random mixtures are investigated in the quenched site and bond Ising model with the ferromagnetic and antiferromagnetic exchange interactions by the high-temperature series expansion of the susceptibility for the d-dimensional simple hypercubical lattices. (d = 2, 3, 4, 5, 6)

DOI: 10.1143/ptp.67.689

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Progress of Theoretical Physics

High Temperature Series Expansion of the Susceptibility of the d-Dimensional Random Ising Model

Shigeru Okamoto, T. Oguchi, Yohtaro Ueno

Published Feb 1, 1982• 2 citations

Publisher

Abstract

DOI: 10.1143/ptp.67.689

Related papers

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A formalism is given whereby high-temperature series for the random-field Ising model on a

d

-dimensional hypercubic lattice is obtained by a partitioning of the vertices of the pure-Ising-series diagrams. For a bimodal distribution of quenched random fields we determine the series for the susceptibility to seventh order. Order by order the disorder is treated exactly.

Dlog

Pad\'e analyses give a susceptibility exponent $\ensuremath{\gamma}$ in

d=3

which crosses over from 1.24 in the pure limit to 1.40 as disorder increases.

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

) for small λ.

{J}_{1}

and

{J}_{2}

. By studying a wide range of coupling ratios

{J}_{2}/{J}_{1}

we obtain compelling evidence for a critical behavior of the form $\ensuremath{\chi}\ensuremath{\sim}{t}^{\ensuremath{-}7/4}|\mathrm{ln}t{|}^{7/8}$, as predicted theoretically by Shalaev, Shankar, and Ludwig.