Timeline for Proving the Replica Trick works
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14 at 15:43 | comment | added | Shannon Starr | There is a famous paper by van Hemmen and Palmer that states much of what is here: The replica method and solvable spin glass model, J.Phys.A, Math Gen. 1979. | |
| Jun 23, 2023 at 9:38 | vote | accept | Felix Benning | ||
| Jun 23, 2023 at 8:49 | comment | added | Carlo Beenakker | so you assume that you are somehow able to calculate the moments of $Z$ without taking the large-$N$ limit? typically, if the problem is simple enough that this is possible, then the whole "replica trick" is not needed, you can just as well average $\log Z$ directly. | |
| Jun 23, 2023 at 7:13 | comment | added | Felix Benning | So if we remain with the first flavour (a mathematical tool to calculate the moment generating function of the logarithm of a random variable), then the steps I put together are alright? Because that is a neat result already. Although my complex analysis is too weak to come up with good sufficient condition for the moment generating function to be holomorphic. I really need to read a book on complex analysis at some point | |
| Jun 23, 2023 at 7:08 | comment | added | Felix Benning | I see, although the wikipedia article seems to ignore that part as well. I interpret this as: there are two flavours of the replica trick. The first one is described by wikipedia for which "in all cases where the replica method can be compared with other exact solutions, the methods lead to the same results" (wikipedia) and the one you describe of which "the validity of the replica trick is doubtful. The most obvious analytic continuation, obtained under the replica symmetric (RS) ansatz, sometimes leads to the wrong results" (paper you posted) | |
| Jun 22, 2023 at 11:48 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |