Related papers: Critical surface of the hexagonal polygon model
We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic…
In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a $2N\times N$ rectangular box with a boundary…
We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain…
The critical behaviour of three-dimensional semi-infinite Ising ferromagnets at planar surfaces with (i) random surface-bond disorder or (ii) a terrace of monatomic height and macroscopic size is considered. The Griffiths-Kelly-Sherman…
We consider the surface critical behaviour of diagonally layered Ising models on the square lattice where the inter-layer couplings follow some aperiodic sequence. The surface magnetisation is analytically evaluated from a simple formula…
Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over…
A three dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices,…
The critical phase surface of a system, in general, can depend on one or more parameters. We show that by calculating the Gini index ($g$) of any suitably defined response function of a system, the critical phase surface can always be…
Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling…
The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom\'e lattice is solved by establishing a mapping correspondence with the eight-vertex model. Letting the parameter of uniaxial single-ion anisotropy tend to infinity, the model…
We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line…
In the Ising model on the simple cubic lattice, we describe the inverse temperature $\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of…
We defined exponential maps with one parameter, associated with geodesics on the parameter surface. By group theory we proposed a formula of the critical points, which is a direct sum of the Lie subalgebras at the critical temperature. We…
Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the O$(n)$ models on the simple-cubic lattice with $n=1$, 2, and 3, i.e. the Ising, XY, and Heisenberg models. For the critical couplings we find…
We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman's spinor method to calculate low-temperature series expansions for the partition function to high order. From these we can obtain…
We investigate magnetic properties of the ferromagnetic Ising model on square-triangle tilings to explore how the hyperuniformity, which characterizes long-range behavior of the point pattern, influences critical phenomena where long-range…
We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes,…
Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and…
We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number…
We study the surface critical behavior of semi-infinite quenched random Ising-like systems at the special transition using three dimensional massive field theory up to the two-loop approximation. Besides, we extend up to the next-to leading…