Revisiting the replica trick: Competition between spin glass and conventional order
arXiv:2302.01361 · doi:10.1007/s10955-023-03135-1
Abstract
There is an ambiguity in how to apply the replica trick to spin glass models which have additional order parameters unrelated to spin glass order -- with respect to which quantities does one minimize vs maximize the action, and in what sequence? Here we show that the correct procedure is to first maximize with respect to "replica" order parameters, and then minimize with respect to "conventional" order parameters. With this result, we further elucidate the relationship between quenched free energies, annealed free energies, and replica order -- it is possible for the quenched and annealed free energies to differ even while all replica order parameters remain zero.
arXiv commentUpdated following referee comments and publication
References in corpus (17)
- Comments on the Sachdev-Ye-Kitaev model
- Spin-Glass Theory for Pedestrians
- Statistical physics of inference: Thresholds and algorithms
- An Extended Variational Principle for the SK Spin-Glass Model
- Simple Glass Models and their Quantum Annealing
- The Quantum Spherical p-Spin-Glass Model
- Does the SYK model have a spin glass phase?
- Clustering of non-ergodic eigenstates in quantum spin glasses
- The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models
- Quantum phase transition in spin glasses with multi-spin interactions
- Quantum algorithm for energy matching in hard optimization problems
- From second to first order transitions in a disordered quantum magnet
- Random subcubes as a toy model for constraint satisfaction problems
- On the replica structure of Sachdev-Ye-Kitaev model
- Out of equilibrium Phase Diagram of the Quantum Random Energy Model
- An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
- Annealed averages in spin and matrix models