Related papers: X(5) Critical-Point Structure in a Finite System
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
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…
Properties of quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Special emphasis is paid to the dynamics at the critical-point of a general first-order phase transition.
We consider properties of critical points in the interacting boson model, corresponding to flat-bottomed potentials as encountered in a second-order phase transition between spherical and deformed $\gamma$-unstable nuclei. We show that…
We discuss the dynamics of finite systems within molecular dynamics models. Signatures of a critical behavior are analyzed and compared to experimental data both in nucleus-nucleus and metallic cluster collisions. We suggest the possibility…
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of…
On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…
We show that critical systems of finite size develop a fractal structure in momentum space with anomalous dimension given in terms of the isotherm critical exponent delta of the corresponding infinite system. The associated power laws of…
Let $f:M\rightarrow M$ be a biholomorphisms on two--dimensional a complex manifold, and let $X\subseteq M$ be a compact $f$--invariant set such that $f|X$ is asymptotically dissipative and without sinks periodic points. We introduce a…
Davidson potentials of the form $\beta^2 +\beta_0^4/\beta^2$, when used in the E(5) framework, bridge the U(5) and O(6) symmetries, while they bridge the U(5) and SU(3) symmetries when used in the X(5) framework. Using a variational…
It is discussed how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be defined and classified for finite systems from the topology of the energy surface…
Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid collective…
A gamma-rigid version (with gamma=0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation…
When interfaces between ordered domains are ordered clusters, frustration disappears. A phase with mixed ordered structures emerges but no length scale can be associated to. We show that sum of densities of each structure plays the role of…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume-Capel…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
On the basis of exactly solvable models with the tricritical and critical endpoints I discuss the physical mechanism of endpoints formation which is similar to the usual liquids. It is demonstrated that the necessary condition for the…
We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a new cluster algorithm, valid for Z(N) models with odd values of N. The two-dimensional Z(5) vector model is conjectured to…