Related papers: Ising exponents from the functional renormalisatio…
The entanglement entropy of the random transverse-field Ising model is calculated by a numerical implementation of the asymptotically exact strong disorder renormalization group method in 2d, 3d and 4d hypercubic lattices for different…
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…
We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its…
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 review the assumptions on which the Monte Carlo renormalization technique is based, in particular the analyticity of the block spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the…
In planar lattice statistical mechanics models like coupled Ising with quartic interactions, vertex and dimer models, the exponents depend on all the Hamiltonian details. This corresponds, in the Renormalization Group language, to a line of…
We show that the functional renormalization group (FRG) allows for the calculation of the probability distribution function of the sum of strongly correlated random variables. On the example of the three-dimensional Ising model at…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The…
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…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $\xi_\parallel$ in the direction…
Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high statistics Monte Carlo simulation for several values of the dilution. The results support the…
It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region";…
Scalar field theories with $\mathbb{Z}_{2}$-symmetry are the traditional playground of critical phenomena. In this work these models are studied using functional renormalization group (FRG) equations at order $\partial^2$ of the derivative…
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…
It was recently shown [Phys. Rev. Lett. {\bf 110}, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming…
We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with…
We compute critical exponents in a $Z_2$ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new…