Related papers: Restoring isotropy in a three-dimensional lattice …
We investigate the nature of the critical behaviour of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition…
We construct a conformal map from $\mathbb{R}^3$ to a three-dimensional spheriod, which includes $\mathbb{S}^3$, a double-cover of the 3-ball, and $\mathbb{R} \times \mathbb{S}^2$ as limiting cases. Using the data of the critical…
We consider a bilayer quantum spin model with anisotropic intra-layer exchange couplings. By varying the anisotropy, the quantum critical phenomena changes from XY to Heisenberg to Ising universality class, with two, three and one modes…
The critical behavior of the order-disorder phase transition in the buckled dimer structure of the Si(001) surface is investigated both theoretically by means of first-principles calculations and experimentally by spot profile analysis…
In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the $(d+s)$-dimensional unit cubic lattice $\Z^{d+s}$, at inverse temperature $\beta=1$ and with coupling constants $J_s>0$ and $J_d>0$ for edges of…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
We consider the conformal bootstrap for spacetime dimension $1<d<2$. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed $\epsilon$-expansion and…
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently,…
We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have…
The ordinary surface magnetic phase transition is studied for the exactly solvable anisotropic spherical model (ASM), which is the limit D \to \infty of the D-component uniaxially anisotropic classical vector model. The bulk limit of the…
Zamolodchikov found an integrable field theory related to the Lie algebra E$_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E$_8$ in the…
The mixed spin-(1/2, S) Ising model on the union jack (centered square) lattice is investigated by establishing the mapping relationship with its corresponding eight-vertex model. An interplay between the nearest-neighbour interaction, the…
We clarify universal critical properties of delocalization-localization transitions in three-dimensional (3D) unitary and orthogonal classes with particle-hole and/or chiral symmetries (classes AIII, BDI, D, C and CI). We first introduce…
We study the bulk and finite-size critical behavior of the O$(n)$ symmetric $\phi^4$ theory with spatially anisotropic interactions of non-cubic symmetry in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class, two-scale…
We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients), which are required in an evaluation of thermodynamic quantities from…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the…
We construct a density functional for the lattice gas / Ising model on square and cubic lattices based on lattice fundamental measure theory. In order to treat the nearest-neighbor attractions between the lattice gas particles, the model is…
In this work we studied the critical behavior of the critical point as function of the number of nearest neighbors on two dimensional regular lattices. We performed numerical simulations on triangular, hexagonal and bilayer square lattices.…
For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have…