Search results for " critical point"
showing 10 items of 55 documents
Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model.
2007
We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point.We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.
On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations
2016
In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.
Multiple solutions for a discrete boundary value problem involving the p-Laplacian.
2008
Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.
Universal low-temperature behavior of the CePd_{1-x}Rh_x ferromagnet
2007
The heavy-fermion metal CePd_{1-x}Rh_x evolves from ferromagnetism at x=0 to a non-magnetic state at some critical concentration x_c. Utilizing the quasiparticle picture and the concept of fermion condensation quantum phase transition (FCQPT), we address the question about non-Fermi liquid (NFL) behavior of ferromagnet CePd_{1-x}Rh_x and show that it coincides with that of both antiferromagnet YbRh_2(Si_{0.95}Ge_{0.05})_2 and paramagnet CeRu_2Si_2 and CeNi_2Ge_2. We conclude that the NFL behavior being independent of the peculiarities of specific alloy, is universal, while numerous quantum critical points assumed to be responsible for the NFL behavior of different HF metals can be well redu…
Ordering phenomena and phase transitions in the physisorbed quantum systems H2, HD and D2
1991
Abstract Recent experimental results of H2, HD and D2 films physisorbed on graphite are briefly reviewed. In particular, the monolayer phase diagrams, the order-disorder transition of the commensurate (C) phase and the commensurate-incommensurate (C-IC) transition are discussed. It will be shown that the melting transition of the C phase belongs to the three-state Potts universality class, and that the C-IC transition occurs via a series of novel intermediate phase, which could be identified as density-modulated phases characterized by striped and hexagonal patterns of domain walls. Due to this rich variety of phenomena, the hydrogen isotopes can be considered as model systems for two-dimen…
Energy scales and magnetoresistance at a quantum critical point
2009
The magnetoresistance (MR) of CeCoIn_5 is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization etc) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the abov…
Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model
1994
A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.
Three solutions for a two-point boundary value problem with the prescribed mean curvature equation
2015
The existence of at least three classical solutions for a parametric ordinary Dirichlet problem involving the mean curvature operator are established. In particular, a variational approach is proposed and the main results are obtained simply requiring the sublinearity at zero of the considered nonlinearity.
Baryon Asymmetry Resulting from FCQPT in the Early Universe
2014
This Chapter does not follow the main line of the book that is the theory of HF compounds but illustrates how the ideas of FC may be applicable to describe a very dissimilar system. Namely, here we consider a novel mechanism for explaining the matter-antimatter asymmetry of the universe. We assume that the universe starts from completely symmetric state and then, as it cools down, it undergoes a quantum phase transition, which in turn causes an asymmetry between matter and anti-matter. As we shall see the quantum phase transition is represented by FCQPT. The mechanism does not require the baryon number violating interactions or \({\textit{CP}}\) violation at a microscopic level. The state F…
A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields
2005
We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.