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An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…
We investigate the effects of quenched disorder, in the form of site and bond dilution, on the physics of the $S=1/2$ antiferromagnetic Heisenberg model on even-leg ladders. Site dilution is found to prune rung singlets and thus create…
In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)].…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor…
The spin-1/2 quantum Ising chain in a transverse random magnetic field is studied by means of the density-matrix renormalization group. The system evolves from an ordered to a paramagnetic state as the amplitude of the random field is…
We briefly review the Ising model with uncorrelated, quenched random-site or random-bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent alpha, which characterizes the…
We investigate the impact of quenched disorder in the critical $O(2)$ vector model. We first review, in the modern language of Conformal Perturbation Theory, the random temperature perturbation in $4-\epsilon$. Then, we present a direct…
We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional,…
It is known rigorously that the phase transition of the $q$-state ferromagnetic Potts model on the square lattice is second order for $q=4$. Despite this fact, some observables of the $q=4$ model show features of a first-order phase…
We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated…
We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We have investigated the correlation functions of interacting bosons at the generic superfluid-insulator transition, a prototypical quantum phase transition, in two dimensions in the spherical limit. Unexpectedly the spatial correlation…
The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform disorder is investigated by intensive Monte Carlo simulations. Taking into account finite-time corrections to scaling, simple ageing behaviour is…
In random quantum magnets, like the random transverse Ising chain, the low energy excitations are localized in rare regions and there are only weak correlations between them. It is a fascinating question whether these correlations are…
We introduce a two-dimensional short-range correlated disorder that is the natural generalization of the well-known one-dimensional dual random dimer model [Phys. Rev. Lett 65, 88 (1990)]. We demonstrate that, as in one dimension, this…
We have studied spin-spin correlation functions in the ordered phase of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the first-order transition point $\beta_t$. Through extensive Monte Carlo simulations we obtain…
The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site,…