Search results for "critical phenomena"
showing 10 items of 91 documents
Longitudinal and Transverse Correlation Functions in the 4 Model below and near the Critical Point
2010
We have extended our method of grouping Feynman diagrams (GFD theory) to study the transverse and longitudinal correlation functions G⊥(k) and G‖(k) in φ model below the critical point (T < Tc) in the presence of an infinitesimal external field. Our method allows a qualitative analysis without cutting the perturbation series. The long-wave limit k → 0 has been studied at T < Tc, showing that G⊥(k) a k−λ⊥ and G‖(k) b k−λ‖ with exponents d/2 < λ⊥ < 2 and λ‖ = 2λ⊥−d are the physical solutions of our equations at the spatial dimensionality 2 < d < 4, which coincides with the asymptotic solution at T → Tc as well as with a nonperturbative renormalization group (RG) analysis provided in our paper…
A CRITICAL VIEW ON THE PERTURBATIVE RG METHOD
2012
The perturbative renormalization group (RG) treatment of the Ginzburg–Landau model is reconsidered based on the Feynman diagram technique. We derive RG flow equations, exactly calculating all vertices appearing in the perturbative RG transformation of the φ4 model up to the ε3 order of the ε-expansion. The Fourier-transformed two-point correlation function G(k) has been considered. Although the ε-expansion of X(k) = 1/G(k) is well defined on the critical surface, we have revealed an inconsistency with the exact rescaling of X(k), represented as an expansion in powers of k at k →0. This new result can serve as a basis to challenge the correctness of the ε-expansion-based perturbative RG met…
Electroweak phase transition in left-right symmetric models
1998
We study the finite-temperature effective potential of minimal left-right symmetric models containing a bidoublet and two triplets in the scalar sector. We perform a numerical analysis of the parameter space compatible with the requirement that baryon asymmetry is not washed out by sphaleron processes after the electroweak phase transition. We find that the spectrum of scalar particles for these acceptable cases is consistent with present experimental bounds.
Sensitivity of jet quenching to enhancement of the medium opacity near TC
2014
One of the main goals of the study of high transverse momentum (P_T) observables in the context of ultrarelativisic heavy-ion collisions is the determination of properties of the produced QCD matter. In particular, the transport coefficients qhat and ehat, characterizing the interaction of the medium with a high p_T parton, are accessible via high P_T probes. However, a precision extraction of their temperature dependence from current data faces the problem that neither the spacetime geometry of the evolving matter droplet nor the link between thermodynamics and transport coefficients is unambiguously known, and various conjectured scenarios how thermodynamics and transport coefficients beh…
Filtered Dark Matter at a First Order Phase Transition.
2020
We describe a new mechanism of dark matter production in the early Universe, based on the dynamics of a first order phase transition. We assume that dark matter particles acquire mass during the phase transition, making it energetically unfavourable for them to enter the expanding bubbles of the massive phase. Instead, most of them are reflected off the advancing bubble walls and quickly annihilate away in the massless phase. The bubbles eventually merge as the phase transition is completed, and only the dark matter particles which have entered the bubbles survive to constitute the observed dark matter today. This mechanism can produce dark matter with masses from the GeV scale to above the…
The Ising square lattice in aL�M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers
1989
Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the …
Character of the Phase Transition in Thin Ising Films with Competing Walls
1995
By extensive Monte Carlo simulations of a lattice gas model we have studied the controversial nature of the gas-liquid transition of a fluid confined between two parallel plates that exert competing surface fields. We find that the transition is shifted to a temperature just below the wetting transition of a semi-infinite fluid but belongs to the two-dimensional Ising universality class. In between this new type of critical point and bulk criticality, a response function ${x}_{\mathrm{nn}}^{max}$ varying exponentially with $D$ is observed, $\frac{2 \mathrm{ln}{\ensuremath{\chi}}_{\mathrm{nn}}^{max}}{D}={\ensuremath{\ell}}^{\ensuremath{-}1}$, where $\ensuremath{\ell}$ is a new length charact…
Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian
1993
A method to describe the metal-insulator transition (MIT) in disordered systems is presented. For this purpose the statistical properties of the eigenvalue spectrum of the Anderson Hamiltonian are considered. As the MIT corresponds to the transition between chaotic and nonchaotic behavior, it can be expected that the random matrix theory enables a qualitative description of the phase transition. We show that it is possible to determine the critical disorder in this way. In the thermodynamic limit the critical point behavior separates two different regimes: one for the metallic side and one for the insulating side.
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
2001
Abstract A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one c…
Statistical Theories of Phase Transitions
2013
The sections in this article are Introduction Phenomenological Concepts Order Parameters and the Landau Symmetry Classification Second-Order Transitions and Concepts about Critical Phenomena (Critical Exponents, Scaling Laws, etc.) Second-Order Versus First-Order Transitions; Tricritical and other Multicritical Phenomena Dynamics of Fluctuations at Phase Transitions Effects of Surfaces and of Quenched Disorder on Phase Transitions: A Brief Overview Computational Methods Dealing with the Statistical Mechanics of Phase Transitions and Phase Diagrams Models for Order–Disorder Phenomena in Alloys Molecular Field Theory and its Generalization (Cluster Variation Method, etc) Computer Simulation T…