Related papers: Geometric Critical Exponents in Classical and Quan…
We present an accurate numerical determination of the crossover from classical to Ising-like critical behavior upon approach of the critical point in three-dimensional systems. The possibility to vary the Ginzburg number in our simulations…
Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the dynamics, from the existence of an attractor-repeller pair…
We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…
Dynamical phase transitions are nonequilibrium counterparts of thermodynamic phase transitions and share many similarities with their equilibrium analogs. In continuous phase transitions, critical exponents play a key role in characterizing…
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
In both quantum computing and black hole physics, it is natural to regard some deformations, infinitesimal unitaries, as \emph{easy} and others as \emph{hard}. This has lead to a renewed examination of right-invariant metrics on…
The critical exponents and the critical amplitude ratio of the scalar model are determined using finite-temperature field theory with auxiliary mass. A new numerical method is developed to solve an evolution equation. The results are…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the…
In two different phase transition models of nuclear fragmentation we show that the emission of pre-equilibrium particles and mixing of events from different classes cannot be ignored in the analysis of nuclear fragmentation data in terms of…
Critical properties of quantum Hall systems are affected by the presence of extra edge channels - present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using…
We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
Results of large-scale Monte Carlo simulations of three-dimensional Ising models with edges and corners are reviewed. At the ordinary transition, angle dependent critical exponents are observed, whereas at the surface transition edge and…