Related papers: Universal sextic effective interaction at critical…
We provide analytical arguments showing that the non-perturbative approximation scheme to Wilson's renormalisation group known as the derivative expansion has a finite radius of convergence. We also provide guidelines for choosing the…
On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to…
The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with…
We have defined a new type of clustering scheme preserving the connectivity of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving process. Our new clustering scheme performs much better for correlation length and…
The scaling form of the free-energy near a critical point allows for the definition of various thermodynamical amplitudes and the determination of their dependence on the microscopic non-universal scales. Universal quantities can be…
The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension $\log_{4} 12 \approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic…
We study the behavior of the renormalized sextic coupling at the intermediate and strong coupling regime for the $\phi^4 $ theory defined in $d=2$-dimension. We found a good agreement with the results obtained by the field-theoretical…
The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln \tau\sim…
A field-theoretical description of the behavior of compressible Ising systems with long-range interactions is presented. The description is performed in the two-loop approximation in three dimensions with the use of the Pade-Borel…
According to renormalization theory, Ising systems above their upper critical dimensionality d_u = 4 have classical critical behavior and the ratio of magnetization moments Q = <m^2>^2 / <m^4> has the universal value 0.456947... However,…
We simulate self-avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths. This allows us to determine the critical value of the renormalized four-point coupling constant in the…
We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on $64^3$, $128^3$, and $256^3$ simple…
Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents…
We propose a method to obtain an improved Hamiltonian (action) for the Ising universality class in three dimensions. The improved Hamiltonian has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling…
We compute the renormalized four-point coupling in the 2d Ising model using transfer-matrix techniques. We greatly reduce the systematic uncertainties which usually affect this type of calculations by using the exact knowledge of several…
We analyze the critical behavior of isotropic systems with dipole-dipole interaction by renormalization-group methods in fixed space-time dimensions. Working in three-dimensional theory we analytically find three-loop expressions for…
Real Space Renormalization Group (RSRG) treatment of Ising model for square and simple cubic lattice is investigated and critical coupling strengths of these lattices are obtained. The mathematical complications, which appear inevitable in…
We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling functions of the magnetization, that is the…
We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the one-component model A. This breakthrough turns out to be possible…
The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG…