Related papers: Quenched free energy in random matrix model
We consider an Ising model with quenched surface disorder, the disorder average of the free energy is the main object of interest. Explicit expressions for the free energy distribution are difficult to obtain if the quenched surface spins…
We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
We model the effects of a large number of zero modes for $N_f$ species of quarks at finite vacuum angle $\theta$, using a matrix model with gaussian weights constrained by the topological susceptibility and compressibility. The quenched…
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary…
The quenched free energy, $F_Q(T){=}{-}T\langle \ln Z(T)\rangle$, of various JT gravity and supergravity theories is explored, taking into account the key non-perturbative physics that is accessible using their matrix model formulations.…
We develop a random sampling method for calculating the time evolution of the R\'{e}nyi entanglement entropy after a quantum quench from an insulating state in free boson systems. Because of the non-Gaussian nature of the initial state,…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
We study the Cauchy directed polymer model on $\mathbb{Z}^{1+1}$, where the underlying random walk is in the domain of attraction to the $1$-stable law. We show that, if the random walk satisfies certain regularity assumptions and its…
Based on the general analysis of the grand canonical partition function in the S-matrix framework, the calculated results on symmetry energy, free energy and entropy of dilute warm nuclear matter are presented. At a given temperature and…
The bootstrap method has proven useful for a wide range of matrix models. Here, we show that the computed momenta can be used to reconstruct the underlying eigenvalue probability distribution, which in turn allows us to compute the free…
Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii)…
Inspired by recent lattice calculations, we model certain aspects of the $\theta$-vacuum using a matrix model with gaussian weights. The vacuum energy exhibits a cusp at $\theta <\pi$ that is sensitive to both the accuracy of the numerical…
We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Renyi entanglement entropies of a one-dimensional gas…
We devise automated workflows for the calculation of Helmholtz and Gibbs free energies and their temperature and pressure dependence and provide the corresponding computational tools. We employ non-equilibrium thermodynamics for evaluating…
The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz…
The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
We discuss the use of the replica ansatz in computing free energies in random matrix theory, and confirm a conjectured condition on analytic continuation in the replica index at large-N.
We obtain an exact formula for the equilibrium free energy of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a heat bath of independent quantum harmonic…