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Behavior in d=2

 

It is also interesting to study the behavior directly in two dimensions, in which tex2html_wrap_inline3162 . This is the lower critical dimension, and may therefore be purely thermal or contain a ``marginal'' glassy phase.

While the general belief is that the latter holds (in this phase-slip free model), there is as yet no agreement in detail on the properties of this phase. A RG treatment was performed some time ago by Cardy and Ostlund in a different context, and appears to provide a sound description of a finite temperature fixed line describing a glassy phase. This predicts tex2html_wrap_inline3718 fluctuations of tex2html_wrap_inline3438 , and more recently has been extended to probe the susceptibility and sensitivity to temperature changes. Various RSB approaches, however, are in conflict with these results, and generally give only tex2html_wrap_inline3722 variations of the phase. Numerical simulations performed so far have not observed the predicted tex2html_wrap_inline3718 fluctuations, and in fact disagree in other ways with the expected signatures of the glass transition. The resolution of these discrepancies is unclear.





Leon Balents
Thu May 30 08:21:44 PDT 1996