Related papers: The Exact Renormalization Group and First-Order Ph…
In this paper the entanglement and quantum phase transition of the anisotropic s=1/2 XY model are studied by using the quantum renormalization group method. By solving the renormalization equations, we get the trivial fixed point and the…
We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
Matter exhibits phases and their transitions. These transitions are classified as first-order phase transitions (FOPTs) and continuous ones. While the latter has a well-established theory of the renormalization group, the former is only…
At first order phase transitions the transition proceeds through droplet nucleation and growth. We discuss a lattice method for calculating the droplet nucleation rate, including the complete dynamical factors. The method is especially…
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
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…
For the three-dimensional cubic model, the nonlinear susceptibilities of the fourth, sixth, and eighth orders are analyzed and the parameters \delta^(i) characterizing their reduced anisotropy are evaluated at the cubic fixed point. In the…
We study the high-temperature phase transitions for the Abelian and $SU(2)$ Higgs models, using the exact renormalization group. The evolution equation for a properly-defined coarse-grained free energy is solved. The phase diagram of the…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
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…
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
The renormalization group functions are calculated in $D=4-\epsilon$ dimensions for the $\phi^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal…
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase…
First-order phase transitions that proceed via nucleation of bubbles are described by the homogeneous nucleation theory of Langer. The nucleation rate is one of the most interesting parameters of these transitions. In previous works we have…
In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading…
We present a new method for calculating the bubble nucleation rate in first order phase transitions non-perturbatively on the lattice. The method takes into account all fluctuations and the full dynamical pre-factor. We also present results…