Related papers: Reconstruction of symmetric Potts Models
We study the low-degree hardness of broadcasting on trees. Broadcasting on trees has been extensively studied in statistical physics, in computational biology in relation to phylogenetic reconstruction and in statistics and computer science…
Random Constraint Satisfaction Problems exhibit several phase transitions when their density of constraints is varied. One of these threshold phenomena, known as the clustering or dynamic transition, corresponds to a transition for an…
Stable Marriage is a fundamental problem to both computer science and economics. Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage…
We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the $\mathbb{Z}_2$-orbifold of the…
In this paper, we apply the form factor bootstrap approach to branch point twist fields in the $q$-state Potts model for $q\leq 3$. For $q=3$ this is an integrable interacting quantum field theory with an internal discrete $\mathbb{Z}_3$…
Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin…
We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
After a brief review of the motivations for grand unification, I discuss the main challenges facing realistic SUSY GUT model building. Achieving doublet-triplet splitting without fine--tuning is chief among them. Symmetry breaking should…
The main result of this paper is that the isomorphism for omega-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical. This strengthens a recent result by Hjorth, Khoussainov,…
The stratified resampling mechanism is one of the resampling schemes commonly used in the resampling steps of particle filters. In the present paper, we prove a central limit theorem for this mechanism under the assumption that the initial…
A variety of algorithms have been proposed for reconstructing trees that show the evolutionary relationships between species by comparing differences in genetic data across present-day taxa. If the leaf-to-leaf distances in a tree can be…
We consider the problem of structure recovery in a graphical model of a tree where some variables are latent. Specifically, we focus on the Gaussian case, which can be reformulated as a well-studied problem: recovering a semi-labeled tree…
Within quantum mechanics model we study the problem of resummation of an asymptotic perturbation series for bound state parameters via optimization of the perturbative expansion. A possible application of the method to the positronium…
We analyse in depth an $S_3$-invariant nearest-neighbor quantum chain in the region of a U(1)-invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to…
The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators.…
The vicinity of the critical point of the three-state Potts model on a Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence that the critical point is integrable is given.
We consider the $U_q[SU(2)]$ symmetric Heisenberg chain when $q=e^{i\pi/(m+1)}$ and $m$ is integer. We consider the cases $m=3$ and $m=5$ which correspond to the Ising and 3-state Potts models. We study the finite size scaling (FSS) of the…
We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in…
We study two $Q$-state Potts models coupled by the product of their energy operators, in the regime $2 < Q \le 4$ where the coupling is relevant. A particular choice of weights on the square lattice is shown to be equivalent to the…