Definition of quenched data set/disoprder in the context of spin glass

Question

I cannot come across a good definition of what "quenched" means in the context of spin glass problems. I see such use as "quenched connectivity", "quenched data set", "quenched disorder"... It seems like the term is overloaded. Is there a good definition of quenched in this context and what does it apply to: data, connectivity matrix, type of system dynamics?

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It is intuitive to think that quenched means the opposite of annealing in a way that annealing is adiobatic, while quenching is, I would guess, instant stress to the system. However, these are my assumptions that are based on a general definition of quenching, not scientific. It does not explain what is quenched data set.

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Later I found a good reference where, in the very first subsection, quenched disorder is well-defined through physics phenomenology. I thought this will be helpful to others. In case this link ever gets moved, the name of the paper is "Spin-glass theory for pedestrians" by Castellani and Cavagna.

Answer 1

Quenched disorder simply means that the disorder is explicitly present in the Hamiltonian, typically under the form of random couplings among the degrees of freedom. For instance, if we consider the famous Edwards-Anderson model $$ H = -\sum_{\langle i, j \rangle} J_{ij} \sigma_i \sigma_j,$$ where $J_{ij}$ are random variables drawn from some probability distribution, the disorder is indeed quenched, meaning that the $J$ are constant on the time scale over which the $\sigma$ fluctuate.

For a nice discussion on quenched disorder (which is the case of relevance for spin glasses) and its distinction from annealed disorder, I would recommend taking a look at Sec. 2 of the paper Spin-Glass Theory for Pedestrians by Tommaso Castellani, and Andrea Cavagna.