Related papers: Random-field Ising and $O(N)$ models: Theoretical …
We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG…
Series for the Wilson functions of an ``environmentally friendly'' renormalization group are computed to two loops, for an $O(N)$ vector model, in terms of the ``floating coupling'', and resummed by the Pad\'e method to yield crossover…
Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well…
A general case of a spatially nonuniform planar layered Ising model, or an equivalent quantum Ising chain, is analysed with an exact functional real space renormalization group. Various surface, finite size, quasiperiodic and random layer…
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 set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
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…
Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its…
The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $\varphi^{3}$ theory that its instability fixed points with…
We give a pedagogical introduction into the functional renormalization group treatment of disordered systems. After a review of its phenomenology, we show why in the context of disordered systems a functional renormalization group treatment…
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static…
The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-\epsilon dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
The critical behavior of three-dimensional weakly diluted quenched Ising model is examined on the base of six-loop renormalization group expansions obtained within the minimal subtraction scheme in $4-\epsilon$ space dimensions. For this…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization-group theory is one of the greatest achievements of theoretical physics. However, the predictions of the theory above an…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
We consider a quantum two-dimensional O(N)xO(2)/O(N-2)xO(2) nonlinear sigma model for frustrated spin systems and formulate its 1/N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions,…
We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) theory within the minimal subtraction scheme in two loop…