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I am a graduate student in mathematics working in probability (without a very good background in physics honestly) and I've started to see arguments based on computations derived from the replica trick. I understand that it is non-rigorous but it appears that a decent number of the solutions one obtains using this trick can be made rigorous by other (often fairly involved) methods. I would like to work on developing a better heuristic approach to problems, so I would like to understand when I can reasonably expect this type of argument to give reasonably accurate predictions. Perhaps more importantly for me, is there a nice characterization of physical situations when it is clear that this trick should fail?

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