ABSTRACT
It is exceedingly tempting to try to relate the dramatic changes in various properties of a liquid undergoing a glass transition in the laboratory at finite cooling rates to an underlying ideal structural glass (STG) transition which would occur (at least in good glass formers) at a finite temperature upon infinitely slow cooling.1 Many scenarios of this kind have been constructed over the years.1-7 Recently, we have developed a picture of an ideal STG transition based on mean-field theories of the STG transition8-10 and on the mean-field theory of the random Potts glass11,12 (PG) and related p-spin models.13 Having given in to the temptation of assuming an ideal STG transition, one is forced to consider what the scaling arguments used for equilibrium phase transitions might say about such an ideal glass transition and, perhaps, about laboratory glass transitions. In this paper we will further explore the concept of an ideal STG transition us ing scaling notions together with concepts arising from our earlier investigations of mean-field theories of structural glasses and of mean-field spin-glass models without reflection symmetry.
