Related papers: Real-Space Renormalization Group Study of the Two-…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
We study the low-energy physics of the critical (2+1)-dimensional random transverse-field Ising model. The one-dimensional version of the model is a paradigmatic example of a system governed by an infinite-randomness fixed point, for which…
We report on numerical simulations of the two-dimensional spin-$1$ Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the…
We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip…
We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of…
We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
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 study the critical behavior and phase diagram of the $d$-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional…
We have adjusted the Density Matrix Renormalization method to handle two dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we…
The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on…
Quenched randomness can lead to robust non-equilibrium phases of matter in periodically driven (Floquet) systems. Analyzing transitions between such dynamical phases requires a method capable of treating the twin complexities of disorder…
The phase diagram and the thermodynamics of the random field Ising model (RFIM) defined on a family of diamond hierarchical lattices of arbitrary dimension and scaling factor $b=2$ is investigated. The phase diagram is studied considering…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
We study quantum corrections to Friedmann-Robertson-Walker cosmology with a scalar field under the assumption that the dynamics are subject to renormalisation group improvement. We use the Bianchi identity to relate the renormalisation…
We consider the Blume-Capel model with zero chemical potential and small magnetic field in a two-dimensional torus whose length increaseswith the inverse of the temeprature. We prove the mestastable behavior and that starting from a…
Criticality in the class of disordered systems comprising the random-field Ising model (RFIM) and elastic manifolds in a random environment is controlled by zero-temperature fixed points that must be treated through a functional…
The critical behavior of the semi-infinite Blume-Capel and Blume-Emery-Griffiths models is investigated in the pair approximation of the Cluster Variation Method. Equations for bulk and surface order parameters and n.n. correlation…
We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction…
Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea…