We derive and prove exponential and form factor expansions of the row correlation function σ0,0σ0,N and the diagonal correlation function σ0,0σN,N of the two dimensional Ising model.

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin [14] for domain wall boundary conditions, we examine some modifications of these boundary conditions. To be precise, we discuss partial domain wall boundary conditions, reflecting ends and half turn boundary conditions (domain wall boundary conditions with half turn symmetry). arXiv:1711.07905v2 [cond-mat.stat-mech] 9 May 2018

The fourth virial coefficient is calculated exactly for a fluid of hard spheres in odd dimensions up to 11.

Abstract. We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles in the disordered and antiferromagnetic regimes where frozen corners appear. At the free fermion point we present an exact finite-size formula for the density on the horizontal edges that relies on the imaginary time transfer matrix approach. In all cases where exact analytic forms for the density and the arctic curves are known the numerical method shows perfect agreement with them. This also suggests the possibility of its use for accurate quantitative purposes. ‡