相关论文: Exact finite-size corrections in the dimer model o…

The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size $L\times M$ and temperature. We start with the dimer method of…

We consider the asymmetric six--vertex model, {\it i.e.} the symmetric six--vertex model in an external field with both horizontal and vertical components, and the relevant asymmetric $XXZ$ chain. The model is widely used to describe the…

The exact analytical lattice results for the partition function of the free neutral scalar field in one spatial dimension in both the configuration and the momentum space were obtained in the framework of the path integral method. The…

We present analyses of substantially extended series for both interacting self-avoiding walks (ISAW) and polygons (ISAP) on the square lattice. We argue that these provide good evidence that the free energies of both linear and ring…

Rail-yard graphs are a general class of graphs introduced in \cite{bbccr} on which the random dimer coverings form Schur processes. We study asymptotic limits of random dimer coverings on rail yard graphs with free boundary conditions on…

In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…

Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic…

In this manuscript we deal with regularity issues and the asymptotic behaviour (as $p \to \infty$) of solutions for elliptic free boundary problems of $p-$Laplacian type ($2 \leq p< \infty$): \begin{equation*} -\Delta_p u(x) +…

We derive rigorously explicit formulas of the Casimir free energy at finite temperature for massless scalar field and electromagnetic field confined in a closed rectangular cavity with different boundary conditions by zeta regularization…

We describe a $p$-dimensional conformal defect of a free Dirac fermion on a $d$-dimensional flat space as boundary conditions on a conformally equivalent space $\mathbb{H}^{p+1} \times \mathbb{S}^{d-p-1}$. We classify allowed boundary…

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the…

Under the Riemann Hypothesis for Dirichlet L-functions, we improve on the error term in a smoothed version of an estimate for the density of elliptic curves with square-free $\Delta=D/16$, where D is the discriminant, by T.D. Browning and…

We analyse the finite-size corrections to the free energy of crystals with a fixed center of mass. When we explicitly correct for the leading ($\ln N/N$) corrections, the remaining free energy is found to depend linearly on 1/N.…

Consider the problem \begin{eqnarray*} -\Delta u_\e &=& v_\e^p \quad v_\e>0\quad {in}\quad \Omega, -\Delta v_\e &=& u_\e^{q_\e}\quad u_\e>0\quad {in}\quad \Omega, u_\e&=&v_\e\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where…

A new computational strategy is proposed to approximate, with a simple but accurate expression, the Maier- Saupe free energy for nematic order. Instead of the traditional approach of expanding the free energy with a truncated Taylor series,…

It has recently been demonstrated that locality of spatial supports in the parametrization of coefficients in elliptic PDEs can lead to improved convergence rates of sparse polynomial expansions of the corresponding parameter-dependent…

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local…

The surface free energies, interfacial tensions and correlation lengths of the Andrews-Baxter-Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary…

The thermodynamics of a scalar field with a quartic interaction is studied within the linear delta expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates…

We study limit shapes for dimer models on domains of the hexagonal lattice with free boundary conditions. This is equivalent to the large deviation phenomenon for a random stepped surface over domains fixed only at part of the boundary.