Related papers: Reconstruction for the Asymmetric Ising Model on R…
Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$ descendants. The…
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the…
We calculate equilibrium solutions for Ising spin models on `small world' lattices, which are constructed by super-imposing random and sparse Poissonian graphs with finite average connectivity c onto a one-dimensional ring. The nearest…
The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…
We study a model of random weighted uniform spanning trees on the complete graph with $n$ vertices, where each edge is assigned a weight of $n^{1+\gamma}$ with probability $1/n$ and $1$ otherwise. Whenever $\gamma$ is large enough, we prove…
We study the ferromagnetic Ising model on the infinite $d$-regular tree under the free boundary condition. This model is known to be a factor of IID in the uniqueness regime, when the inverse temperature $\beta\ge 0$ satisfies $\tanh \beta…
The tree reconstruction problem is to collect and analyze massive data at the $n$th level of the tree, to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. Its connection to the clustering problem in…
We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on…
Averaged spin-spin correlation function squared $\overline{<\sigma(0)\sigma(R)>^{2}}$ is calculated for the ferromagnetic random bond Potts model. The technique being used is the renormalization group plus conformal field theory. The…
We study the magnetization for the classical antiferromagnetic Ising model on the Shastry-Sutherland lattice using the tensor renormalization group approach. With this method, one can probe large spin systems with little finite-size effect.…
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…
Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete,…
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
We study several statistical mechanical models on a general tree. Particular attention is devoted to the classical Heisenberg models, where the state space is the d-dimensional unit sphere and the interactions are proportional to the…