Gaussian Random Bond Problem for Annealed System in 1/n Expansion

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Abstract
Critical phenomena for the for the annealed n-vector model are studied in 1/n expansion by assuming that the exchange interactions between spins are fluctuating variables obeying the Gaussian distribution. It is shown that for an overall fluctuation of the interaction between spins the susceptibility never diverges at any finite temperature except for n→∞ (spherical limit) and n=1 (Ising) cases. On the other hand, if the fluctuation is restricted to only nearest-neighbor pairs, the susceptibility is proved to diverge at an appropriate transition temperature in the limit n→∞. The critical exponent γ in this case is shown to be the same as the spherical model value. Also the dependence of transition temperature on the strength of fluctuation is discussed.

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