Phase separation in the six-vertex model with a variety of boundary conditions

Abstract

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

Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition

“…Thus, the south-west portion of the curve is obtained by the transformations µ → −µ, x → x, y → 2−y in (90) and therefore the whole curve is a semicircle centered at (1, 1) with unit radius (see Figure 5). It is worth noting this result is in agreement with Monte Carlo simulations [26] and coincides with the west portion of the arctic curve of the six-vertex model with domain wall boundary conditions in the 2N ×2N square lattice [20].…”

Arctic boundaries of the ice model on three-bundle domains

“…This phenomenon was soon observed to be ubiquitous within the context of highly correlated statistical mechanical systems; see, for instance, [1,2,5,6,7,10,12,13,15,16,17,18,19,20,25,28,29,30,32,33,34,35,42,43,44,45,51,54,57,61]. In particular, Cohn-Kenyon-Propp developed a variational principle [12] that prescribes a law of large numbers for random domino tilings on almost arbitrary domains, which was used effectively by to explicitly determine the arctic boundaries of uniformly random lozenge tilings on polygonal domains.…”

Boundary correlations for the six-vertex model with reflecting end boundary condition

“…Besides of its own relevance, the knowledge of boundary correlation functions could be useful in the analytical investigation of the arctic curves. It is worth noting that the spatial phase separation for the reflecting end boundary was recently studied numerically [28] and the results confirm the expectations for phase separation, however, there are no analytical results for the arctic curves. Although it seems not possible to have full control on the boundary conditions at the current experimental level, the reflecting end boundary condition is an important case to study, since its determinant form [25] allows for exact analytical results for the physical quantities at finite lattice sizes and also in the thermodynamic limit.…”