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Journal of the Physical Society of Japan

Absence of Spin Glass Ordering in Some Random Spin Systems

Yukiyasu Ozeki, Hidetoshi Nishimori

Published Dec 15, 1988• 10 citations
Publisher

Abstract

We discuss the improvement of the imperfect argument of Schuster for the absence of spin glass ordering at and below four dimensions in short-range continuous spin systems, and propose a condition for his method to be justified. Assuming satisfaction of the above condition, we apply the method to long-range interactions to reproduce the phase diagram drawn by a renormalization group approach. In particular the three-dimensional RKKY system is found to be at the lower critical dimension. Effects of exchange and uniaxial anisotropies are discussed. The latter anisotropy is shown not to induce transverse spin glass ordering if the system is not ordered in the , x y -plane by the exchange interaction.

DOI
10.1143/jpsj.57.4255

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The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite-dimensional spin glasses with short-range interactions. The defect energy renormalization-group equations derived for it by Kotliar, Anderson, and Stein have been reexamined and a new fixed point has been found. The fixed points which have previously been studied are found to be inappropriate. It is shown that the renormalization-group equations themselves directly imply that that the spin-glass phase is replica symmetric, in agreement with droplet model expectations, when the range exponent $\ensuremath{\sigma}$ lies between the upper and lower critical values.
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