



01495nas a2200121   4500008004100000245005200041210005100093260001500144520112900159100002901288700001901317856003701336       2019                        eng d00aQuenched vs Annealed: Glassiness from SK to SYK0 aQuenched vs Annealed Glassiness from SK to SYK  c11/26/20193 a<p>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 &quot;annealed&quot; phase to a &quot;non-annealed&quot; phase as a function of temperature. We further show that this effect appears only at O(N)&#39;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.</p>1 aBaldwin, Christopher, L.1 aSwingle, Brian  uhttps://arxiv.org/abs/1911.11865