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In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems.…
The perturbative renormalization of the Ginzburg-Landau model is reconsidered based on the Feynman diagram technique. We derive renormalization group (RG) flow equations, exactly calculating all vertices appearing in the perturbative…
The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange…
We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse…
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
In the present paper, we proposed a simple spin-1/2 model which provides a exactly solvable example to study the Ising criticality with central charge c=1/2. By mapping it onto the real Majorana fermions, the Ising critical behavior is…
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two point observables of the one dimensional Ising model without…
A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
We revisit the two dimensional non-Abelian Thirring model in order to investigate its fixed point structure and the corresponding renormalization group (RG) flow. For this purpose we discuss the bosonization of the model, and we present…
We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we…
We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First we recover the known properties of the traditional model with…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
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…
To avoid the complicated topology of surviving clusters induced by standard Strong Disorder RG in dimension $d>1$, we introduce a modified procedure called 'Boundary Strong Disorder RG' where the order of decimations is chosen a priori. We…
Motivated by the renormalization group (RG) approach to $c=0$ matrix model of Bre\'zin and Zinn-Justin, we develop a RG scheme for $c=1$ matrix model on a circle and analyze how the two coupling constants in double scaling limit with…
We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasi-statically changing the applied source at…
We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…
We study a renormalization group (RG) map for tensor networks that include two-dimensional lattice spin systems such as the Ising model. Numerical studies of such RG maps have been quite successful at reproducing the known critical…