相关论文: Strict convexity of the free energy for non-convex…

We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles.…

We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate…

State space geometry is obtained for the one dimensional Blume Emery Griffiths model and the associated scalar curvature(s) investigated for various parameter regimes, including the Blume-Capel limit and the Griffiths model limit. For the…

An explicit formula for the interaction energy of $n$ vortices in the abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the…

To our best knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex…

Three different vortex glass models are studied by examining the energy barrier against vortex motion across the system. In the two-dimensional gauge glass this energy barrier is found to increase logarithmically with system size which is…

Collective lattice dynamics determine essential aspects of condensed matter, such as elastic and thermal properties. These exhibit strong dependence on the length-scale, reflecting the marked wavevector dependence of lattice excitations.…

We derive upper bounds on the fluctuations of a class of random surfaces of the $\nabla \phi$-type with convex interaction potentials. The Brascamp-Lieb concentration inequality provides an upper bound on these fluctuations for uniformly…

We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis…

The effects of gauge interactions in graphene have been analyzed up to now in terms of effective models of Dirac fermions. However, in several cases lattice effects play an important role and need to be taken consistently into account. In…

Understanding the contact between solid surfaces is a long standing problem which has a strong impact on the physics of many processes such as adhesion, friction, lubrication and wear. Experimentally, the investigation of solid/solid…

We investigated the thermodynamic properties of graphene in a noncommutative phase-space in the presence of a constant magnetic field. In particular, we determined the behaviour of the main thermodynamical functions: the Helmholtz free…

For the first time the persistent current in a 2D free-electron system has been calculated analytically. The tight binding model is considered on a square lattice with filling factor 1/2. The array has a shape of rectangle with boundary…

In this paper we describe the asymptotic behavior of rigid spin lattice energies by exhibiting a continuous interfacial limit energy as scaling to zero the lattice spacing. The limit is not trivial below a percolation threshold: it can be…

In this paper, we extend the discrete-to-continuum procedure we developed in our previous work to derive a continuum variational model for a hexagonal twisted bilayer material in which one layer is fixed. We use a discrete energy containing…

We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the…

We construct finite-range interactions on $\mathcal{S}^{\mathbb{Z}^2}$, where $\mathcal{S}$ is a finite set, for which the associated equilibrium states (i.e., the shift-invariant Gibbs states) fail to converge as temperature goes to zero.…

Interactions between the different degrees of freedom form the basis of many manifestations of intriguing physics in condensed matter. In this respect, quantifying the dynamics of normal modes that themselves arise from these interactions…

The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface…

We consider a $\varphi$-rigidity property for divergence-free vector fields in the Euclidean $n$-space, where $\varphi(t)$ is a non-negative convex function vanishing only at $t=0$. We show that this property is always satisfied in…