The critical properties of systems under constraint differ from their ideal counterparts through Fisher renormalization. The mathematical properties of Fisher renormalization applied to critical exponents are well known: the renormalized indices obey the same scaling relations as the ideal ones and the transformations are involutions in the sense that re-renormalizing the critical exponents of the constrained system delivers their original, ideal counterparts. Here we examine Fisher renormalization of critical amplitudes and show that, unlike for critical exponents, the associated transformations are not involutions. However, for ratios and combinations of amplitudes which are universal, Fisher renormalization is involutory.
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - 2014|
Bibliographical noteThe full text is available free from the link given. The published version can be found at http://dx.doi.org/10.1088/1742-5468/2014/7/P07011.
- classical phase transitions (theory)
- critical exponents and amplitudes (theory)
Izmailian, N., & Kenna, R. (2014). Universal amplitude ratios for constrained critical systems. Journal of Statistical Mechanics: Theory and Experiment, 2014(7), [P07011]. https://doi.org/10.1088/1742-5468/2014/7/P07011