Related papers: Determinant Formulas for Matrix Model Free Energy
This work builds on Varchenko et al's introduction of bilinear forms for hyperplane arrangements, where the determinant of the associated matrices factorizes into simple components. While one of the determinant formula developed by…
In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such…
With the help of the factorizing $F$-matrix, the scalar products of the $U_q(gl(1|1))$ free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the…
We propose a non-perturbative method for defining the higher dimensional operators which appear in the Heavy Quark Effective Theory (HQET), such that their matrix elements are free of renormalon singularities, and diverge at most…
{We show that the free energy of the three-state $\tau_2(t_q)$ model can be expressed as products of Jacobi elliptic functions, the arguments being those of an hyperelliptic parametrization of the associated chiral Potts model. This is the…
We use genus zero free energy functions of Hermitian matrix models to define spectral curves and their special deformations. They are special plane curves defined by formal power series with integral coefficients generalizing the Catalan…
In the study of free arrangements, the most useful result to construct/check free arrangements is the addition-deletion theorem. Recently, the multiple version of the addition theorem is proved, called the multiple addition theorem (MAT) to…
Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expansion for the formal version of this model, following the…
We present formulas for the homogenous multivariate resultant as a quotient of two determinants. They extend classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the…
We present a new and exploratory approach to determine the $\Delta\beta(\beta)$-shift in the $O(3)$ nonlinear $\sigma$-model. The method is based on a scaling hypothesis for a free energy difference, which is assumed to be valid in a…
This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and…
Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose…
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…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…
The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…
This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this…
We study a simple nonlinear model defined on the honeycomb and triangular lattices. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable…
We present the many-particle Hamiltonian model of Lipkin, Meshkov and Glick in the context of deformed polynomial algebras and show that its exact solutions can be easily and naturally obtained within this formalism. The Hamiltonian matrix…
We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model…