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Journal de physique

Zero temperature magnetization of the random axis chain

Bernard Derrida, Annette Zippelius

Published Jan 1, 1986• 2 citations
Publisher

Abstract

We have calculated the zero temperature magnetization of the random axis chain in the limit of strong anisotropy and small magnetic field h. For the uniform distribution of random axes we obtain m = Ch1/ δ with the same critical exponent δ = 3 as in the one dimensional Ising spinglass with a Gaussian distribution of bonds.
DOI
10.1051/jphys:01986004706095500

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We investigate the one-dimensional long-range random-field Ising magnet with Gaussian distribution of the random fields. In this model, a ferromagnetic bond between two spins is placed with a probability $p\ensuremath{\sim}{r}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\sigma}}$, where rrr is the distance between these spins and $\ensuremath{\sigma}$ is a parameter to control the effective dimension of the model. Exact ground states at zero temperature are calculated for system sizes up to L=219L={2}^{19}L=219 via graph theoretical algorithms for four different values of $\ensuremath{\sigma}\ensuremath{\in}{0.25,0.4,0.5,1.0}$ while varying the strength hhh of the random fields. For each of these values several independent physical observables are calculated, i.e., magnetization, Binder parameter, susceptibility, and a specific-heat-like quantity. The ferromagnet-paramagnet transitions at critical values ${h}_{c}(\ensuremath{\sigma})$ as well as the corresponding critical exponents are obtained. The results agree well with theory, and interestingly we find for $\ensuremath{\sigma}=1/2$ the data is compatible with a critical random-field strength hc>0{h}_{c}>0hc​>0.
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