Related papers: Correct bounds on the Ising lace-expansion coeffic…

We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on ${\mathbb{Z}}^d$. The two-point functions of these models are respectively the generating function for self-avoiding walks from…

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the…

We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building…

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the…

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…

As first asserted by Y. Imry and S-K Ma, the famed discontinuity of the magnetization as function of the magnetic field in the two dimensional Ising model is eliminated, for all temperatures, through the addition of quenched random magnetic…

Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…

We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between plus and minus spins, the scaling limit of these interfaces…

A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents $\nu$ and…

We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…

We consider the critical and off-critical properties at the boundary of the random transverse-field Ising spin chain when the distribution of the couplings and/or transverse fields, at a distance $l$ from the surface, deviates from its…

We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the…

The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (1) when the temperature is larger than the critical temperature of the Ising model…

We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…

We study two exactly solvable two-dimensional conformal models, the critical Ising model and the Sommerfield model, on the lattice. We show that finite-size effects are important and depend on the aspect ratio of the lattice. In particular,…

In this work, we provide a self-contained derivation of the spin-operator matrix elements in the fermionic basis, for the critical periodic Ising chain at a generic system length $N\in 2Z_{\ge 2}$. The approach relies on the near-Cauchy…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane $y>0$ with different boundary conditions $a$ and $b$ on the negative and positive $x$ axes. For $ab=-+$ and $f+$,…

In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the…