Related papers: Nonuniversality in random criticality
In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
While in the fully-connected limit the solution of the spin-glass model is known, with the existence of a complex transition on a critical line in the temperature-external field phase diagram, in finite dimensions we don't know if a…
We study a model for a quantum Ising spin glass in two space dimensions by Monte Carlo simulations. In the disordered phase at $T=0$, we find power law distributions of the local susceptibility and local non-linear susceptibility, which are…
The two-dimensional Ising model is studied at the boundary of a half-infinite cylinder. The three regular lattices (square, triangular and hexagonal) and the three regimes (sub-, super- and critical) are discussed. The probability of having…
At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx…
We investigate the conditions required for general spin systems with frustration and disorder to display self-organized criticality, a property which so far has been established only for the fully-connected infinite-range…
The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic…
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…
The non-equilibrium ageing behaviour of the 3D and 4D critical Ising spin glass is studied for both binary and gaussian disorder. The same phenomenology of the time-dependent scaling as in non-disordered magnets is found but the…
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…
In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural…
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we…
We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same…
We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to…
Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…
The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation where the cut-off is taken to infinity, dimensional regularisation (DR) with minimal subtraction, and DR with…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However 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…