相关论文: Renormalisation group theory applied to $\ddot{x}+…
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…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
We present a renormalization-group (RG) flow argument for s-wave kaon condensation in dense nuclear-star matter predicted in chiral perturbation theory. It is shown that it is the {\it relevant} mass term together with {\it any} attractive…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow…
We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
Renormalization group (RG) and resummation techniques have been used in $N$-component $\phi^4$ theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical…
Hyperuniformity, where the static structure factor obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, emerges at criticality in systems having multiple, symmetry-unrelated, absorbing states. Important examples arise in periodically sheared…
We formulate the next-to-leading order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice, and investigate nonperturbative renormalization group flows in the strong coupling region by diagonalizing…
In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
Critical behaviour of the O(n)-symmetric $\phi^{4}$-model with an antisymmetric tensor order parameter is studied by means of the field-theoretic renormalization group (RG) in the leading order of the $\varepsilon=4-d$-expansion (one-loop…
We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the…
A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…
The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point…
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
A proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations. The formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by…