Quenched vs Annealed: Glassiness from SK to SYK
| Autor: | Brian Swingle, C. L. Baldwin |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics Statistical Mechanics (cond-mat.stat-mech) Condensed matter physics QC1-999 High Energy Physics::Lattice FOS: Physical sciences General Physics and Astronomy Syk Disordered Systems and Neural Networks (cond-mat.dis-nn) Fermion Condensed Matter - Disordered Systems and Neural Networks 01 natural sciences 010305 fluids & plasmas High Energy Physics - Theory (hep-th) 0103 physical sciences Quantum gravity 010306 general physics Condensed Matter - Statistical Mechanics |
| Zdroj: | Physical Review X, Vol 10, Iss 3, p 031026 (2020) |
| ISSN: | 2160-3308 |
| Popis: | We show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space; and second, a replica treatment of two prominent examples which exhibit phase transitions from an "annealed" phase to a "non-annealed" phase as a function of temperature. We further show that this effect appears only at $O(N)$'th order in a $1/N$ expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography. 13 pages of main text, 4 pages of appendix, 4 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|