相关论文: 2D models of statistical physics with continuous s…

With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for…

Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the…

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Euler equations (also known for some particular scenarios as the water wave problem), for which the smoothness of the interface breaks down…

The Cauchy problem for a quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For some simplified formulation of the problem, a criterion for the…

We study the emergence of glassy states after a sudden cooling in lattice models with short range interactions and without any a priori quenched disorder. The glassy state emerges whenever the equilibrium model possesses a sufficient number…

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a…

We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…

We address here a few classical lattice--spin models, involving $n-$component unit vectors ($n=2,3$), associated with a $D-$dimensional lattice $\mathbb{Z}^D,\,D=1,2$, and interacting via a pair potential restricted to nearest neighbours…

The Higgs mechanism of mass generation is the main ingredient in the contemporary Standard Model and its various generalizations. However, there is no comprehensive theory of spontaneous symmetry breaking. We summarize the relevant…

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…

Depending on the coupling to the environment, symmetries of open quantum systems manifest in two distinct forms, the strong and the weak. We study the spontaneous symmetry breaking among phases with strong symmetry, weak symmetry, and no…

It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…

We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A…

We study the dynamics of two strongly-interacting fermions moving in 2D lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon.…

Spontaneous symmetry breaking generally circumvents one-dimensional systems with local interactions in thermal equilibrium. Here, we analyze a category of one-dimensional Hermitian models via local non-Hermitian constructions. Notably,…

The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum mechanical building blocks is one of the cornerstones of modern…

We study coherent and radiative interactions induced among two or more quantum units, by coupling them to two-dimensional lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal…

It is well known that continuous symmetries of quantum fields can be realized non-linearly, e.g. in the context of sigma models, and can also be spontaneously broken on non-compact spacetimes. In this note we study how these effects are…

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such…

Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…