Related papers: Correlation inequalities for the Potts model
It is argued that the classical local inertial frame used to define rotational states of quantum systems is only approximate, and that geometry itself must also be rotationally quantized at the Planck scale. A Lorentz invariant statistical…
In this paper, we study estimation of parameters in a two-parameter Potts model with $q$ colors and coupling matrix $A_N$. We characterize concrete sufficient conditions for existence of the pseudo-likelihood estimator of the Potts model,…
We review the random loop representations of Toth and Aizenman-Nachtergaele for quantum Heisenberg models. They can be combined and extended so as to include the quantum XY model and certain SU(2)-invariant spin 1 systems. We explain the…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
We derive loop equations for the one-link correlators of gauge and scalar fields in the Kazakov-Migdal model. These equations determine the solution of the model in the large N limit and are similar to analogous equations for the Hermitean…
In this survey, we explore how superorthogonality amongst functions in a sequence $f_1,f_2,f_3,\ldots$ results in direct or converse inequalities for an associated square function. We distinguish between three main types of…
We consider the Ashkin-Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the extension that is necessary to prove a…
It is shown in this paper that the G-Condition and the P-Condition from representability imply the fermion correlation estimate from [1] which, in turn, is known to yield a nontrivial bound on the accuracy of the Hartree-Fock approximation…
The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by Jackiw and Pi are generalized using the non-relativistic Kaluza-Klein-type framework…
We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and (4) a classical Ising model with…
We consider the Potts model with $q$ colors on a sequence of weighted graphs with adjacency matrices $A_n$, allowing for both positive and negative weights. Under a mild regularity condition the mean-field prediction for the log partition…
The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also…
We prove Griffiths inequalities for spins in n>1 dimensions with no interaction.
We present new $\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to…
We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or…
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular `gauge boson', connected to…
This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely…
This work presents the building-blocks of an integrability-based representation for multi-point Fishnet Feynman integrals with any number of loops. Such representation relies on the quantum separation of variables (SoV) of a non-compact…
It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory, converge and yield knot invariants. This was…
We consider fractal curves in two-dimensional $Z_N$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main…