One more discussion of the replica trick: the example of the exact solution
Abstract
Systematic replica field theory calculations are analysed using the examples of two particular one-dimensional 'toy' random models with Gaussian disorder. Due to the simplicity of the models an integer n-th power of the partition function can be calculated here exactly. However, further analytic continuation for non-integer values of the replica parameter n inevitably involves the usual replica method of 'cheating', which nevertheless allows us to derive correct and rather non-trivial results for the entire free energy distribution functions both for a finite system size and in the thermodynamic limit.
- Publication:
-
Philosophical Magazine
- Pub Date:
- January 2012
- DOI:
- 10.1080/14786435.2011.582052
- Bibcode:
- 2012PMag...92...16D
- Keywords:
-
- replicas;
- fluctuations;
- disordered systems;
- polymers