Related papers: Field-theoretic Analysis of Dynamic Isotropic Perc…
New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8)…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
Modification of the renormalization-group approach, invoking Stratonovich transformation at each step, is proposed to describe phase transitions in 3D Ising-class systems. The proposed method is closely related to the mean-field…
We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…
We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master…
Universal scaling laws only apply asymptotically near critical phase transitions. We propose a general scheme, based on normal form theory of renormalization group flows, for incorporating corrections to scaling that quantitatively describe…
Nonequilibrium phase transitions are characterized by the so-called critical exponents, each of which is related to a different observable. Systems that share the same set of values for these exponents also share the same universality…
The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition…
We investigate a one-dimensional three-species dynamical model whose dynamics naturally generate the semi-directed percolation cluster in time and show a non-equilibrium absorbing state phase transition from an active to inactive state. The…
The scaling behavior of the entanglement entropy in the two-dimensional random transverse field Ising model is studied numerically through the strong disordered renormalization group method. We find that the leading term of the entanglement…
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…
The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so…
The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach…
Dynamic critical behavior in superfluid systems is considered in a presence of external stirring and advecting processes. The latter are generated by means of the Gaussian random velocity ensemble with white-noise character in time variable…
Universality is a fundamental concept in modern physics. For the $q$-state Potts model, the critical exponents are merely determined by the order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of…
We investigate both analytically and numerically the ensemble of minimum-weight loops and paths in the negative-weight percolation model on random graphs with fixed connectivity and bimodal weight distribution. This allows us to study the…
A coupled phase-oscillator model consists of phase-oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…