Related papers: The Critical Ising Model on a M\"obius Strip
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of…
Recent numerical studies of the susceptibility of the three-dimensional Ising model with various interaction ranges have been analyzed with a crossover model based on renormalization-group matching theory. It is shown that the model yields…
Conformal fields with boundaries give rise to rich critical phenomena that can reveal information about the underlying conformality. While most existing studies focus on Hermitian systems, here we explore boundary critical phenomena in a…
The Ising model is the simplest to describe many-body effects in classical statistical mechanics. Duality analysis leads to a critical point under several assumptions. The Ising model itself has $Z(2)$ symmetry. The basis of the duality…
We revisit the 3-states Potts model on random planar triangulations as a Hermitian matrix model. As a novelty, we obtain an algebraic curve which encodes the partition function on the disc with both fixed and mixed spin boundary conditions.…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…
We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and…
The excess adsorption $\Gamma $ in two-dimensional Ising strips $(\infty \times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various…
We study the Ising model with an external magnetic field on random tetravalent planar maps and investigate its critical behavior. Explicit expressions for spontaneous magnetization and the susceptibility are computed and the critical…
We study a class of nonlocal conformal field theories in two dimensions which are obtained as deformations of the Virasoro minimal models. The construction proceeds by coupling a relevant primary operator $\phi_{r,s}$ of the $m$-th minimal…
We study field-induced phase transitions in the two-dimensional dipolar Ising ferromagnet with a specific ratio between the exchange and dipolar constants, $\delta=1$, which exhibits a stripe-ordered phase with the width of one lattice unit…
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…
It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…
Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase.…
For a given statistical model, the bipartite fidelity $\mathcal F$ is computed from the overlap between the groundstate of a system of size $N$ and the tensor product of the groundstates of the same model defined on two subsystems $A$ and…
The behavior of two-dimensional Ising spin glasses at the multicritical point on triangular and honeycomb lattices is investigated, with the help of finite-size scaling and conformal-invariance concepts. We use transfer-matrix methods on…
The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and…
Recent analyses of least-sensitive inflection points in derivatives of the microcanonical entropy for the two-dimensional Ising model revealed higher-order transition signals in addition to the well-studied second-order…