相关论文: Matrix Models on Large Graphs
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…
The limit free energy of spin-glass models with convex interactions can be represented as a variational problem involving an explicit functional. Models with non-convex interactions are much less well-understood, and simple variational…
We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and CPU and GPU implementations of local optimization, focusing on minima and saddles of index…
Given a graph $M,$ path eigenvalues are eigenvalues of its path matrix. The path energy of a simple graph $M$ is equal to the sum of the absolute values of the path eigenvalues of the graph $M$ (Shikare et. al, 2018). We have discovered new…
We study the matrix model for N M2-branes wrapping a Lens space L(p,1) = S^3/Z_p. This arises from localization of the partition function of the ABJM theory, and has some novel features compared with the case of a three-sphere, including a…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
In some cases, an important example being at finite temperature, extreme infrared, collinear, or light-cone behaviour may cause the usual loop expansion to break down. For some of these cases higher order ladder graphs can become important.…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical…
Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles under the constraints that the expected values of a set of graph observables are equal to given…
We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of…
The 2D off-critical q-state Potts model with boundaries was studied as a factorizable relativistic scattering theory. The scattering S-matrices for particles reflecting off the boundaries were obtained for the cases of ``fixed'' and…
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings and magnetic fields. We prove that the magnetizations,…
Call the sum of the singular values of a matrix A the energy of A. We investigate graphs and matrices of energy close to the maximal one. We prove a conjecture of Koolen and Moulten and give a stability theorem characterizing all square…
The electronic free energies in metal clusters are calculated based on a simple ladder spectrum for the level degeneracies three and four, and compared with the known results for degeneracies one and two. The low temperature and the…
We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed $p$-spin interactions. The upper bound involves a Guerra-style interpolation and requires a convexity assumption on the model's…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
We study the $O(N)$ vector model for scalars with quartic interaction at large $N$ on $S^1\times S^2$ without the singlet constraint. The non-trivial fixed point of the model is described by a thermal mass satisfying the gap equation at…