Related papers: A Multi-Body Dobrushin-Sokal Criterion -- Part I
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties.…
We rigorously examine 2d square lattices composed of Ninf{S} classical spins isotropically coupled. If Hsup{ex},inf{i,j} is the local exchange Hamiltonian each operator exp(-beta.Hsup{ex},inf{i,j}) is expanded on the basis of spherical…
We provide new sufficient conditions for subcriticality of classical and quantum spin lattice systems, formulated in terms of the uniqueness of Kubo-Martin-Schwinger (KMS) states. This is achieved by exploiting a non-commutative analog of…
Orbital degree of freedom plays an important role for understanding quantum many-body phenomena. In this work, we study an experimentally related setup with ultracold bosons loaded into hybridized bands of two-dimensional hexagonal optical…
We present a family of many-body models which are exactly solvable analytically. The models are an extended n-body interaction Lipkin-Meshkov-Glick model which considers spin-flip terms which are associated with the interaction of an…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to…
We study the zero-free regions of the partition function of the hard-core model on finite graphs and their implications for the analyticity of the free energy on infinite lattices. Classically, zero-freeness results have been established up…
Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these…
We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more…
We study interacting one dimensional (1D) quantum lattice gases with integrable impurities. These model Hamiltonians can be derived using the quantum inverse scattering method for inhomogeneous models and are by construction integrable.…
We derive the asymptotic expansion of the partition function of a Coulomb gas system in the determinantal case on compact Riemann surfaces of any genus g. Our main tool is the bosonization formula relating the analytic torsion and geometric…
We develop a systematic perturbation theory for the Helmholtz free energy of a classical $N$-body system within the mesoscopic framework of~\cite{OsanoMeso,OsanoExtensivity}. The combined coarse-graining operator…
We prove necessary and sufficient conditions for lattice Schr\"{o}dinger operators to have a zero energy bound state in arbitrary dimension. The two criteria are sharp, complementary, and depend crucially on both the dimension and…
In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…
This paper is the second in a series devoted to constructing stochastic motions for the two-dimensional $N$-body delta-Bose gas for all integers $N\geq 3$ and establishing the associated Feynman-Kac-type formulas. The main results here…
In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
Using ambient space we develop a fully gauge and o(d,2) covariant approach to boundary values of AdS(d+1) gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e.…
We present exact calculations of the zero-temperature partition function for the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) for families of arbitrarily long strip graphs of the square and triangular lattices…