Permutation invariant matrix quantum thermodynamics and negative specific heat capacities in large N systems
Year: 2024
Type: article
Abstract: A bstract We study the thermodynamic properties of the simplest gauged permutation invariant matrix quantum mechanical system of oscillators, for general matrix size N . In the canonical ensemble, the model has a transition at a temperature T given by $$ x={e}^{-1/T}\sim {x}_c={e}^{-1/{T}_c}=\frac{\log N}{N} $$ x = e − 1 / T ~ x c = e − 1 / T c = log N N , characterised by a sharp peak in the specific heat capacity (SHC), which separates a high temperature from a low temperature region. The peak grows and the low-temperature region shrinks to zero with increasing N . In the micro-canonical ensemble, for finite N , there is a low energy phase with negative SHC and a high energy phase with positive SHC. The low-energy phase is dominated by a super-exponential growth of degeneracies as a function of energy which is directly related to the rapid growth in the number of directed graphs, with any number of vertices, as a function of the number of edges. The two ensembles have matching behaviour above the transition temperature. We further provide evidence that these thermodynamic properties hold in systems with U( N ) symmetry such as the zero charge sector of the 2-matrix model and in certain tensor models. We discuss the implications of these observations for the negative specific heat capacities in gravity using the AdS/CFT correspondence.
Source: Journal of High Energy Physics
Authors: Denjoe O’Connor, Sanjaye Ramgoolam
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405984366