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In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.

@article{Parisi2004, abstract = {In a previous paper we found that in the random field Ising model at zero temperature in three dimensions the correlation length is not self-averaging near the critical point and that the violation of self-averaging is maximal. This is due to the formation of bound states in the underlying field theory. We present a similar study for the case of disordered Potts and Ising ferromagnets in two dimensions near the critical temperature. In the random Potts model the correlation length is not self-averaging near the critical temperature but the violation of self-averaging is weaker than in the random field case. In the random Ising model we find still weaker violations of self-averaging and we cannot rule out the possibility of the restoration of self-averaging in the infinite volume limit.}, annote = {From Duplicate 2 (Scale invariance and self-averaging in disordered systems - Parisi, Giorgio; Picco, Marco; Sourlas, Nicolas) From Duplicate 2 ( Scale invariance and self-averaging in disordered systems - Parisi, Giorgio; Picco, Marco; Sourlas, Nicolas ) }, archivePrefix = {arXiv}, arxivId = {cond-mat/0312715}, author = {Parisi, Giorgio and Picco, Marco and Sourlas, Nicolas}, doi = {10.1209/epl/i2004-10014-0}, eprint = {0312715}, file = {:Users/marco/Library/Application Support/Mendeley Desktop/Downloaded/Parisi, Picco, Sourlas - 2004 - Scale invariance and self-averaging in disordered systems.pdf:pdf}, issn = {0295-5075}, journal = {Europhysics Letters (EPL)}, keywords = {Disordered Systems and Neural Networks,Statistical Mechanics}, month = {may}, number = {4}, pages = {465--470}, primaryClass = {cond-mat}, title = {{Scale invariance and self-averaging in disordered systems}}, url = {http://arxiv.org/abs/cond-mat/0312715 http://stacks.iop.org/0295-5075/66/i=4/a=465?key=crossref.3b96a888f56dac830a3f9022fd5fa6e8}, volume = {66}, year = {2004} }

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