Related papers: Large N expansion of the 2-matrix model, multicut …
This paper discusses the large N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden BRST method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model…
In this paper, a variational perturbation scheme for nonrelativistic many-Fermion systems is generalized to a Bosonic system. By calculating the free energy of an anharmonic oscillator model, we investigated this variational expansion…
We calculate the free energy of a hot gas of electrons and photons to three loops using the hard-thermal-loop perturbation theory reorganization of finite-temperature perturbation theory. We calculate the free energy through three loops by…
We present an explicit formula for the expected value of a product of several independent symplectically invariant matrices in which the trace and real part function may be applied, possibly to different subexpressions. This takes the form…
We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
We study the effective potential of three-dimensional O($N$) models. In statistical physics the effective potential represents the free-energy density as a function of the order parameter (Helmholtz free energy), and, therefore, it is…
An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation…
We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding…
We consider the two-matrix model with potentials whose derivative are arbitrary rational function of fixed pole structure and the support of the spectra of the matrices are union of intervals (hard-edges). We derive an explicit formula for…
We study thermal properties of a large-N massless pion gas using a low-energy QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion mass…
We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number $n$ of fundamental representations of $SU(N)$, and we identify a duality in the representation content of this…
A new method is proposed for the calculation of the free energy of an N-component Phi^4 theory at finite temperature. The method combines a perturbative treatment of the hard modes with a non-perturbative treatment in the effectively…
We solve the puzzle of the disagreement between orthogonal polynomials methods and mean field calculations for random NxN matrices with a disconnected eigenvalue support. We show that the difference does not stem from a Z2 symmetry…
In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy in high temperature QED.…
Due to instanton effects, gauge-theoretic large N expansions yield asymptotic series, in powers of 1/N^2. The present work shows how to generically make such expansions meaningful via their completion into resurgent transseries, encoding…
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 review methods to calculate eigenvalue distributions of products of large random matrices. We discuss a generalization of the law of free multiplication to non-Hermitian matrices and give a couple of examples illustrating how to use…
A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from…
Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We…