Search results for "renormalization group"
showing 10 items of 206 documents
JIMWLK evolution of the odderon
2016
We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numeric…
Ferroelastic transition in Kbr:Kcn studied by neutrons, x-rays and ultrasonic
1986
The ferroelastic phase transition of (KBr) 0 27 (KNC) 0.73 has been studied by X-ray diffraction, ultrasonics and inelastic neutron scattering. It is the first example of a cubic crystal where the elastic shear constant C 44 softens completely corresponding to the m = 2 universality class. C 44 and the Bragg intensities show a non-classical critical behaviour.
Smooth Feshbach map and operator-theoretic renormalization group methods
2003
Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.
Random walks in dynamic random environments and ancestry under local population regulation
2015
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in space-time regions where the medium is typical, we obtain a law of large numbers and an averaged central limit theorem for the walk via a regeneration construction under suitable coarse-graining. Such random walks occur naturally as spatial embeddings of ancestral lineages in spatial population models with local regulation. We verify that our assumptions hold for logistic branching random walks when the population density is sufficiently high.
Critical phenomena at surfaces
1990
Abstract The presence of free surfaces adds a rich and interesting complexity to critical phenomena associated with phase transitions occurring in bulk materials. We shall review Monte Carlo computer simulation studies of surface critical behavior in simple cubic Ising- and XY-models with nearest-neighbor interactions J in the bulk and Js at the surface. These studies allow the identification of various critical exponents and critical amplitude ratios involving both the critical behavior of local quantities and of surface excess corrections to the bulk. We consider both the “ordinary” transition (surface criticality controlled by the bulk) and the “special transition” (a multicritical point…
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice
1997
We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, …
Monte Carlo investigations of phase transitions: status and perspectives
2000
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.
Ordering and demixing transitions in multicomponent Widom-Rowlinson models.
1995
We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not …
The Gauge Glass Transition
1993
Results of Monte Carlo simulations in three and four spatial dimensions of a simple model that seems to have the necessary ingredients for disordered type-II superconductor behavior in an external magnetic field are reported. The data suggest that in d = 3 dimensions there is a finite temperature phase transition at T ≈ 0.45 into a truly superconducting vortex glass phase with infinite d.c. conductivity The (effective) correlation length exponent v and the dynamic critical exponent z at this transition are in good agreement with experiments. In d = 4 dimensions the gauge glass transition is located at T ≈ 0.95. It is concluded that the lack of time reversal symmetry in the model places it i…
Continuous Phase Transitions at Surfaces of CuAu Alloy Models — A Monte Carlo Study of Surface Induced Order and Disorder
1996
The influence of surface on phase transitions has found significant attention in recent years, and a number of excellent reviews exists. [1, 2, 3] A variety of complex phenomena occur which are also related to the physics of adsorption and wetting. The scenario of wetting requires three distinct phases, for instance the vacuum, the bulk phase and a third phase intervening in between at equilibrium. In case of surface induced disorder (SID, a film of disordered layers at the surface “wets” the bulk phase as the temperature approaches the bulk transition temperature T c,b. The transition at the surface may be continuous (standard critical wetting phenomena), and, as theoretically investigated…