Abstract
Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For such systems, it is proven that ind=2 dimensions there can be no first-order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter. Discontinuities which would amount to a continuous symmetry breaking, in systems which are (stochastically) invariant under the action of a continuous subgroup ofO(N), are suppressed by the randomness in dimensionsd≦4. Specific implications are found in the Random-Field Ising Model, for which we conclude that ind=2 dimensions at all (β,h) the Gibbs state is unique for almost all field configurations, and in the Random-Bond Potts Model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point. The results are explained by the argument of Imry and Ma [1]. The proofs involve the analysis of fluctuations of free energy differences, which are shown (using martingale techniques) to be Gaussian on the suitable scale.
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Communicated by A. Jaffe
Dedicated to R. L. Dobrushin, on the occasion of his 60th birthday
Also in the Physics Department
Research partially supported by NSF grants PHY-8896163 and PHY-8912067
Work done in part at Rutgers University, Department of Mathematics
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Aizenman, M., Wehr, J. Rounding effects of quenched randomness on first-order phase transitions. Commun.Math. Phys. 130, 489–528 (1990). https://doi.org/10.1007/BF02096933
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DOI: https://doi.org/10.1007/BF02096933